2026
|
Cônsoli, P. M.; Day-Roberts, E.; Knolle, J.; Botana, A. S.; Erten, O. Tuning the Magnetic Properties of Kitaev Materials via the Antiferromagnetic Proximity Effect: Novel Phases and Application to an α-RuCl3/MnPS3 Bilayer Journal Article Nano Lett. 26, 12491–12499 (2026). @article{consoliTuningMagneticProperties2026,
title = {Tuning the Magnetic Properties of Kitaev Materials via the Antiferromagnetic Proximity Effect: Novel Phases and Application to an α-RuCl_{3}/MnPS_{3} Bilayer},
author = {P. M. Cônsoli and E. Day-Roberts and J. Knolle and A. S. Botana and O. Erten},
url = {https://doi.org/10.1021/acs.nanolett.6c03321},
doi = {10.1021/acs.nanolett.6c03321},
issn = {1530-6984},
year = {2026},
date = {2026-09-08},
urldate = {2026-09-01},
journal = {Nano Lett.},
volume = {26},
number = {37},
pages = {12491–12499},
abstract = {In recent years, the increasing level of control over van der Waals (vdW) heterostructures has opened new routes to tune the properties of quantum materials. Motivated by these developments, we examine the potential consequences of interfacing a Kitaev honeycomb magnet, such as α-RuCl3, with a nearly lattice-matched vdW antiferromagnet. By combining perturbation theory, exact diagonalization, and a classical energy-minimization method, we show that an effective staggered magnetic field originating from the vdW antiferromagnet can drive a monolayer of a Kitaev material into various novel phases, including an antichiral Kitaev spin liquid, a nonmagnetic nematic phase, and different types of skyrmion crystals. We then apply first-principles simulations to assess the prospect of concretely realizing this setup in a heterobilayer of α-RuCl3 and the easy-axis antiferromagnet MnPS3.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In recent years, the increasing level of control over van der Waals (vdW) heterostructures has opened new routes to tune the properties of quantum materials. Motivated by these developments, we examine the potential consequences of interfacing a Kitaev honeycomb magnet, such as α-RuCl3, with a nearly lattice-matched vdW antiferromagnet. By combining perturbation theory, exact diagonalization, and a classical energy-minimization method, we show that an effective staggered magnetic field originating from the vdW antiferromagnet can drive a monolayer of a Kitaev material into various novel phases, including an antichiral Kitaev spin liquid, a nonmagnetic nematic phase, and different types of skyrmion crystals. We then apply first-principles simulations to assess the prospect of concretely realizing this setup in a heterobilayer of α-RuCl3 and the easy-axis antiferromagnet MnPS3. |  |
Belbase, B. P.; Unnikrishnan, A.; Feng, S.; Choi, E. S.; Knolle, J.; Banerjee, A. Finite spinon density of states in triangular lattice delafossite TlYbSe2 Journal Article Phys. Rev. Res. 8, L032021 (2026), datadoi: 10.5281/zenodo.21481296. @article{belbaseFiniteSpinonDensity2026,
title = {Finite spinon density of states in triangular lattice delafossite TlYbSe_{2}},
author = {B. P. Belbase and A. Unnikrishnan and S. Feng and E. S. Choi and J. Knolle and A. Banerjee},
url = {https://link.aps.org/doi/10.1103/tc4h-cq9c},
doi = {10.1103/tc4h-cq9c},
year = {2026},
date = {2026-08-11},
urldate = {2026-08-01},
journal = {Phys. Rev. Res.},
volume = {8},
number = {3},
pages = {L032021},
publisher = {American Physical Society},
abstract = {We introduce the rare-earth delafossite compound TlYbSe2 — extending the search for quantum spin liquids in frustrated triangular lattice magnets. While the dc magnetization suggests magnetic exchange interactions on the order of several kelvin, the zero-field ac magnetization and heat capacity measurements reveal no signs of long-range magnetic order down to 20 mK, indicating a quantum-disordered ground state. We observe a spin-freezing transition near ∼30mK at zero field that is suppressed by an applied magnetic field of ∼0.02T. A broad anomaly in the heat capacity measurements between 2 and 5 K is indicative of short-range spin correlations. Below 350 mK, we observe a robust linear temperature dependence of the heat capacity, accompanied by the complete absence of long-range order at low fields. We propose that a phenomenological theory, based on the interplay between spinons and thermally excited gauge flux excitations, can account for the linear temperature dependence of the heat capacity, and could be widely applicable to similar critical quantum spin liquid candidate materials. The results establish the low-temperature, low-field regime of TlYbSe2 as a prime candidate for field-tunable triangular quantum spin liquid behavior and highlight the importance of thermally excited gauge field excitations.},
note = {datadoi: 10.5281/zenodo.21481296},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We introduce the rare-earth delafossite compound TlYbSe2 — extending the search for quantum spin liquids in frustrated triangular lattice magnets. While the dc magnetization suggests magnetic exchange interactions on the order of several kelvin, the zero-field ac magnetization and heat capacity measurements reveal no signs of long-range magnetic order down to 20 mK, indicating a quantum-disordered ground state. We observe a spin-freezing transition near ∼30mK at zero field that is suppressed by an applied magnetic field of ∼0.02T. A broad anomaly in the heat capacity measurements between 2 and 5 K is indicative of short-range spin correlations. Below 350 mK, we observe a robust linear temperature dependence of the heat capacity, accompanied by the complete absence of long-range order at low fields. We propose that a phenomenological theory, based on the interplay between spinons and thermally excited gauge flux excitations, can account for the linear temperature dependence of the heat capacity, and could be widely applicable to similar critical quantum spin liquid candidate materials. The results establish the low-temperature, low-field regime of TlYbSe2 as a prime candidate for field-tunable triangular quantum spin liquid behavior and highlight the importance of thermally excited gauge field excitations. | |
Feng, S.; Zhu, P.; Knolle, J.; Knap, M. Transient localization from fractionalization: Vanishingly small energy transport in gapless quantum magnets Journal Article Phys. Rev. B 114, 034423 (2026), datadoi: 10.5281/zenodo.17151126. @article{fengTransientLocalizationFractionalization2026,
title = {Transient localization from fractionalization: Vanishingly small energy transport in gapless quantum magnets},
author = {S. Feng and P. Zhu and J. Knolle and M. Knap},
url = {https://doi.org/10.1103/crq3-l1r3},
doi = {10.1103/crq3-l1r3},
year = {2026},
date = {2026-07-21},
urldate = {2026-07-21},
journal = {Phys. Rev. B},
volume = {114},
number = {3},
pages = {034423},
abstract = {In this work, we investigate zero-temperature energy transport in a gapless quantum magnet. We find that suppressed energy transport can arise at low frequencies due to transient localization from fractionalization, even in the absence of extrinsic defects or disorder. Concretely, we consider a Kitaev ladder model, whose spin degrees of freedom fractionalize into visons and spinons, in a uniform magnetic field. For moderate magnetic fields, visons are heavy and act as quasistatic disorder that induces transient localization of light spinons even in the translation-invariant model and at zero temperature, which strongly suppresses the residual transport.},
note = {datadoi: 10.5281/zenodo.17151126},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In this work, we investigate zero-temperature energy transport in a gapless quantum magnet. We find that suppressed energy transport can arise at low frequencies due to transient localization from fractionalization, even in the absence of extrinsic defects or disorder. Concretely, we consider a Kitaev ladder model, whose spin degrees of freedom fractionalize into visons and spinons, in a uniform magnetic field. For moderate magnetic fields, visons are heavy and act as quasistatic disorder that induces transient localization of light spinons even in the translation-invariant model and at zero temperature, which strongly suppresses the residual transport. |  |
Bader, T.; Feng, S.; Budaraju, S.; Becca, F.; Knolle, J.; Pollmann, F. Triangular J1-J2 Heisenberg antiferromagnet in a magnetic field Journal Article Phys. Rev. B 113, L241114 (2026), datadoi: 10.5281/zenodo.20510149. @article{baderTriangular$J_1textensuremathJ_2$Heisenberg2026,
title = {Triangular J_{1}-J_{2} Heisenberg antiferromagnet in a magnetic field},
author = {T. Bader and S. Feng and S. Budaraju and F. Becca and J. Knolle and F. Pollmann},
url = {https://link.aps.org/doi/10.1103/rwhz-jf5b},
doi = {10.1103/rwhz-jf5b},
year = {2026},
date = {2026-06-18},
urldate = {2026-06-01},
journal = {Phys. Rev. B},
volume = {113},
number = {24},
pages = {L241114},
publisher = {American Physical Society},
abstract = {The behavior of the paradigmatic 𝐽1−𝐽2 triangular lattice Heisenberg antiferromagnet in a magnetic field remains unsettled despite decades of study. We map out the phase diagram using three complementary approaches, including self-consistent nonlinear spin-wave theory, density-matrix renormalization group, and variational Monte Carlo. This combined analysis resolves the competition among different field-induced magnetic orders and magnetization plateaus across the classically frustrated parameter range. In particular, there is a finite range in the parameter regime around 𝐽2/𝐽1 = 1/8 in which (i) upon the application of the external field, the gapless quantum spin liquid acquires a finite density of monopoles, and (ii) by further increasing the field, two plateaus are clearly obtained at 𝑚=1/3 and 𝑚=1/2. We discuss the experimental importance of the consecutive magnetization plateau transitions as a signature of an underlying quantum spin-liquid phase.},
note = {datadoi: 10.5281/zenodo.20510149},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The behavior of the paradigmatic 𝐽1−𝐽2 triangular lattice Heisenberg antiferromagnet in a magnetic field remains unsettled despite decades of study. We map out the phase diagram using three complementary approaches, including self-consistent nonlinear spin-wave theory, density-matrix renormalization group, and variational Monte Carlo. This combined analysis resolves the competition among different field-induced magnetic orders and magnetization plateaus across the classically frustrated parameter range. In particular, there is a finite range in the parameter regime around 𝐽2/𝐽1 = 1/8 in which (i) upon the application of the external field, the gapless quantum spin liquid acquires a finite density of monopoles, and (ii) by further increasing the field, two plateaus are clearly obtained at 𝑚=1/3 and 𝑚=1/2. We discuss the experimental importance of the consecutive magnetization plateau transitions as a signature of an underlying quantum spin-liquid phase. | |
Khodaeva, U. E.; Kovrizhin, D. L.; Knolle, J. Quantum critical dynamical response of the twisted Kitaev spin chain Journal Article Phys. Rev. B 113, 045120 (2026), datadoi: 10.5281/zenodo.15722856. @article{khodaevaQuantumCriticalDynamical2026,
title = {Quantum critical dynamical response of the twisted Kitaev spin chain},
author = {U. E. Khodaeva and D. L. Kovrizhin and J. Knolle},
url = {https://link.aps.org/doi/10.1103/884v-7tqh},
doi = {10.1103/884v-7tqh},
year = {2026},
date = {2026-01-12},
urldate = {2026-01-01},
journal = {Phys. Rev. B},
volume = {113},
number = {4},
pages = {045120},
publisher = {American Physical Society},
abstract = {The dynamical structure factor of the transverse field Ising model (TFIM) shows universal power-law divergence at its quantum critical point, signatures of which have been arguably observed in inelastic neutron scattering studies of quantum spin chain materials, for example CoNb2O6. However, it has recently been suggested that its microscopic description is better captured in terms of a twisted Kitaev spin chain (TKSC) with bond-anisotropic couplings. Here, we present exact results for the dynamical structure factor of the TKSC across its quantum critical point, analyzing both the universal low-frequency response and the non-universal high-energy features. In addition, we explore extensions of the model including broken glide symmetry as well as the case of random, and incommensurate magnetic fields. Notably, in the latter case, the fermionic excitations exhibit a localization-delocalization transition, which is manifest in the dynamical response as a distinct signature at finite frequency. We discuss the relevance of these features for the observation of quantum critical response in experiments.},
note = {datadoi: 10.5281/zenodo.15722856},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The dynamical structure factor of the transverse field Ising model (TFIM) shows universal power-law divergence at its quantum critical point, signatures of which have been arguably observed in inelastic neutron scattering studies of quantum spin chain materials, for example CoNb2O6. However, it has recently been suggested that its microscopic description is better captured in terms of a twisted Kitaev spin chain (TKSC) with bond-anisotropic couplings. Here, we present exact results for the dynamical structure factor of the TKSC across its quantum critical point, analyzing both the universal low-frequency response and the non-universal high-energy features. In addition, we explore extensions of the model including broken glide symmetry as well as the case of random, and incommensurate magnetic fields. Notably, in the latter case, the fermionic excitations exhibit a localization-delocalization transition, which is manifest in the dynamical response as a distinct signature at finite frequency. We discuss the relevance of these features for the observation of quantum critical response in experiments. | |
Pazmino, E. I.; Feng, S.; Dhakal, R.; Rousochatzakis, I.; Winter, S. M.; Knolle, J.; Tsirlin, A. A. Beyond Kitaev exchange: Γ'-driven magnetism in Ag3LiRh2O6 Unpublished (2026), arXiv:2610.19770. @unpublished{pazminoKitaevExchangeGammadriven2026,
title = {Beyond Kitaev exchange: Γ'-driven magnetism in Ag_{3}LiRh_{2}O_{6}},
author = {E. I. Pazmino and S. Feng and R. Dhakal and I. Rousochatzakis and S. M. Winter and J. Knolle and A. A. Tsirlin},
url = {https://arxiv.org/abs/2610.19770},
doi = {10.48550/arXiv.2610.19770},
year = {2026},
date = {2026-10-14},
urldate = {2026-10-14},
abstract = {In Kitaev magnets, frustration arises from bond-dependent spin anisotropic interactions, which can potentially realize sought-after quantum spin liquid phases. However, material realizations with dominating Kitaev exchange are scarce and the broad parameter space of extended Kitaev models remains largely unexplored experimentally. Here, we use density-functional theory, cluster many-body, spin-wave, and density-matrix renormalization calculations to show that the recently discovered honeycomb rhodate Ag3LiRh2O6 hosts an off-diagonal exchange Γ′1 that is second in magnitude only to the ferromagnetic Kitaev exchange K1. This combination of K1 and Γ′1 explains key experimental observations, an unusually high magnetic ordering temperature of 94 K at ambient pressure and its rapid decrease under hydrostatic pressure as Ag3LiRh2O6 evolves from ferromagnetic toward zigzag order within the honeycomb planes. Our spin-wave calculations further predict an unusual topology of the magnon bands arising from the Γ′1 term in the spin Hamiltonian of the honeycomb layer. We show that the large trigonal splitting of t2g states enhances Γ′1, the hitherto underappreciated term in Kitaev magnets, and opens the way to new interesting regimes of the extended Kitaev model.},
note = {arXiv:2610.19770},
keywords = {},
pubstate = {published},
tppubtype = {unpublished}
}
In Kitaev magnets, frustration arises from bond-dependent spin anisotropic interactions, which can potentially realize sought-after quantum spin liquid phases. However, material realizations with dominating Kitaev exchange are scarce and the broad parameter space of extended Kitaev models remains largely unexplored experimentally. Here, we use density-functional theory, cluster many-body, spin-wave, and density-matrix renormalization calculations to show that the recently discovered honeycomb rhodate Ag3LiRh2O6 hosts an off-diagonal exchange Γ′1 that is second in magnitude only to the ferromagnetic Kitaev exchange K1. This combination of K1 and Γ′1 explains key experimental observations, an unusually high magnetic ordering temperature of 94 K at ambient pressure and its rapid decrease under hydrostatic pressure as Ag3LiRh2O6 evolves from ferromagnetic toward zigzag order within the honeycomb planes. Our spin-wave calculations further predict an unusual topology of the magnon bands arising from the Γ′1 term in the spin Hamiltonian of the honeycomb layer. We show that the large trigonal splitting of t2g states enhances Γ′1, the hitherto underappreciated term in Kitaev magnets, and opens the way to new interesting regimes of the extended Kitaev model. | |
Guo, J.; Brizolla, G. M. S.; Rao, P.; Shao, J.; Huang, X. H.; Meier, T. N. G.; Xu, T.; Ji, P.; Finley, J.; Fabian, J.; Knolle, J.; Back, C.; Chen, L. Electric-current control of anomalous Hall effect Unpublished (2026), arXiv: 2601.03744. @unpublished{guoElectriccurrentControlAnomalous2026,
title = {Electric-current control of anomalous Hall effect},
author = {J. Guo and G. M. S. Brizolla and P. Rao and J. Shao and X. H. Huang and T. N. G. Meier and T. Xu and P. Ji and J. Finley and J. Fabian and J. Knolle and C. Back and L. Chen},
url = {https://arxiv.org/abs/2601.03744},
doi = {10.48550/arXiv.2601.03744},
year = {2026},
date = {2026-08-26},
urldate = {2026-08-01},
abstract = {We demonstrate robust and reversible electric-current control of the anomalous Hall effect (AHE) in a two-dimensional WTe2/Fe3GeTe2 (FGT) stack. Applying a current through Td-WTe2 leads to a giant modulation of the AHE of the adjacent FGT layer, with the relative change of the AHE conductivity exceeding 180},
note = {arXiv: 2601.03744},
keywords = {},
pubstate = {published},
tppubtype = {unpublished}
}
We demonstrate robust and reversible electric-current control of the anomalous Hall effect (AHE) in a two-dimensional WTe2/Fe3GeTe2 (FGT) stack. Applying a current through Td-WTe2 leads to a giant modulation of the AHE of the adjacent FGT layer, with the relative change of the AHE conductivity exceeding 180 |  |
Wiener, T.; Brunner, L.; Heyl, M. Universal symmetry-breaking dynamics at continuous phase transitions: Evidence for a new dynamical critical exponent Unpublished (2026), arXiv: 2605.07753
datadoi: 10.5281/zenodo.18862010. @unpublished{wiener2026universalsymmetrybreakingdynamicscontinuous,
title = {Universal symmetry-breaking dynamics at continuous phase transitions: Evidence for a new dynamical critical exponent},
author = {T. Wiener and L. Brunner and M. Heyl},
url = {https://arxiv.org/abs/2605.07753},
doi = {10.48550/arXiv.2605.07753},
year = {2026},
date = {2026-07-03},
urldate = {2026-07-01},
abstract = {Uncovering and understanding universal dynamics in matter far from equilibrium remains a key challenge. In this work, we identify a so far unrecognized form of universal behavior that emerges after a sudden symmetry-breaking quench at continuous phase transitions. Our key observation is that the order-parameter fluctuations in Ising models exhibit a compelling temporal collapse across a wide range of system sizes and quench strengths, indicative of an emergent single-variable scaling form. This phenomenon can be explained by introducing a so far unknown dynamical critical exponent for the underlying continuous phase transition. We find evidence for a lower critical effective dimension of this universal regime: it is observed in the 2D quantum and 3D and 4D classical Ising models, but not in the 1D quantum or 2D classical cases. Our results suggest that our observed universal far-from-equilibrium scaling may extend beyond the Ising models studied here and could more broadly characterize systems with non-conserved order parameters, opening new avenues for exploring universal dynamics both theoretically and in current experimental platforms.},
note = {arXiv: 2605.07753
datadoi: 10.5281/zenodo.18862010},
keywords = {},
pubstate = {published},
tppubtype = {unpublished}
}
Uncovering and understanding universal dynamics in matter far from equilibrium remains a key challenge. In this work, we identify a so far unrecognized form of universal behavior that emerges after a sudden symmetry-breaking quench at continuous phase transitions. Our key observation is that the order-parameter fluctuations in Ising models exhibit a compelling temporal collapse across a wide range of system sizes and quench strengths, indicative of an emergent single-variable scaling form. This phenomenon can be explained by introducing a so far unknown dynamical critical exponent for the underlying continuous phase transition. We find evidence for a lower critical effective dimension of this universal regime: it is observed in the 2D quantum and 3D and 4D classical Ising models, but not in the 1D quantum or 2D classical cases. Our results suggest that our observed universal far-from-equilibrium scaling may extend beyond the Ising models studied here and could more broadly characterize systems with non-conserved order parameters, opening new avenues for exploring universal dynamics both theoretically and in current experimental platforms. | |
Guo, J.; Rao, P.; Huang, X.; Xu, T.; Guo, Y.; Shao, J.; Sun, C.; Orekhov, A.; Meier, T. N. G.; Knolle, J.; Back, C. H.; Chen, L. Current-tunable room temperature ferromagnetism and current-driven phase transitions Unpublished (2026), arXiv:2603.27298. @unpublished{guoCurrenttunableRoomTemperature2026-03-282026,
title = {Current-tunable room temperature ferromagnetism and current-driven phase transitions},
author = {J. Guo and P. Rao and X. Huang and T. Xu and Y. Guo and J. Shao and C. Sun and A. Orekhov and T. N. G. Meier and J. Knolle and C. H. Back and L. Chen},
url = {https://arxiv.org/abs/2603.27298},
doi = {10.48550/arxiv2603.27298},
year = {2026},
date = {2026-03-28},
urldate = {2026-03-01},
publisher = {arXiv},
abstract = {It is generally assumed that the application of a charge-current in ferromagnetic metals suppresses their ferromagnetic order through trivial Joule heating. Here, we demonstrate that a charge current can instead enhance magnetic ordering. Using a WTe2/Fe3Ge2Te (FGT) stack as a model system, we show that a charge current flowing in WTe2 controls the ferromagnetic properties and magnetic phase transition of the adjacent FGT via a current-induced effective magnetic-field arising from orbital magnetization. Remarkably, the charge current drives a substantial enhancement of the Curie temperature, boosting it well above room temperature. Furthermore, we show that the charge-current enables controlled tuning of the phase transitions in FGT, which confirms the scaling behaviour of a ferromagnet-paramagnet phase transition. This work provides a pathway for integrating two-dimensional ferromagnets into spintronic functionalities at technologically relevant temperatures and for exploring novel current-driven phenomena in ferromagnetic systems.},
note = {arXiv:2603.27298},
keywords = {},
pubstate = {published},
tppubtype = {unpublished}
}
It is generally assumed that the application of a charge-current in ferromagnetic metals suppresses their ferromagnetic order through trivial Joule heating. Here, we demonstrate that a charge current can instead enhance magnetic ordering. Using a WTe2/Fe3Ge2Te (FGT) stack as a model system, we show that a charge current flowing in WTe2 controls the ferromagnetic properties and magnetic phase transition of the adjacent FGT via a current-induced effective magnetic-field arising from orbital magnetization. Remarkably, the charge current drives a substantial enhancement of the Curie temperature, boosting it well above room temperature. Furthermore, we show that the charge-current enables controlled tuning of the phase transitions in FGT, which confirms the scaling behaviour of a ferromagnet-paramagnet phase transition. This work provides a pathway for integrating two-dimensional ferromagnets into spintronic functionalities at technologically relevant temperatures and for exploring novel current-driven phenomena in ferromagnetic systems. | |
2025
|
Neehus, A.; Rosch, A.; Knolle, J.; Seifert, U. F. P. Projectively Implemented Altermagnetism in an Exactly Solvable Quantum Spin Liquid Journal Article Phys. Rev. Lett. 135, 256504 (2025), datadoi: 10.5281/zenodo.15231830. @article{neehusProjectivelyImplementedAltermagnetism2025,
title = {Projectively Implemented Altermagnetism in an Exactly Solvable Quantum Spin Liquid},
author = {A. Neehus and A. Rosch and J. Knolle and U. F. P. Seifert},
url = {https://link.aps.org/doi/10.1103/cnk8-vnxg},
doi = {10.1103/cnk8-vnxg},
year = {2025},
date = {2025-12-19},
urldate = {2025-12-01},
journal = {Phys. Rev. Lett.},
volume = {135},
number = {25},
pages = {256504},
publisher = {American Physical Society},
abstract = {Altermagnets are a new class of symmetry-compensated magnets with large spin splittings. Here, we show that the notion of altermagnetism extends beyond the realm of Landau-type order: we study exactly solvable ℤ2 quantum spin(-orbital) liquids (QSLs), which simultaneously support magnetic long-range order as well as fractionalization and ℤ2 topological order. Our symmetry analysis reveals that in this model three distinct types of “fractionalized altermagnets (AM*)” emerge, which can be distinguished by their residual symmetries. Importantly, the fractionalized excitations of these states carry an emergent ℤ2 gauge charge, which implies that they transform projectively under symmetry operations. Consequently, we show that “altermagnetic spin splittings” are now encoded in a momentum-dependent particle-hole asymmetry of the fermionic parton bands. We discuss consequences for experimental observables such as dynamical spin structure factors and (nonlinear) thermal and spin transport.},
note = {datadoi: 10.5281/zenodo.15231830},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Altermagnets are a new class of symmetry-compensated magnets with large spin splittings. Here, we show that the notion of altermagnetism extends beyond the realm of Landau-type order: we study exactly solvable ℤ2 quantum spin(-orbital) liquids (QSLs), which simultaneously support magnetic long-range order as well as fractionalization and ℤ2 topological order. Our symmetry analysis reveals that in this model three distinct types of “fractionalized altermagnets (AM*)” emerge, which can be distinguished by their residual symmetries. Importantly, the fractionalized excitations of these states carry an emergent ℤ2 gauge charge, which implies that they transform projectively under symmetry operations. Consequently, we show that “altermagnetic spin splittings” are now encoded in a momentum-dependent particle-hole asymmetry of the fermionic parton bands. We discuss consequences for experimental observables such as dynamical spin structure factors and (nonlinear) thermal and spin transport. | |
Rao, P.; Knolle, J.; Classen, L. Van Hove singularities and competing instabilities in an altermagnetic metal Journal Article Phys. Rev. B 112, 235140 (2025), datadoi: 10.5281/zenodo.17868124. @article{zfk4-rxh1,
title = {Van Hove singularities and competing instabilities in an altermagnetic metal},
author = {P. Rao and J. Knolle and L. Classen},
url = {https://link.aps.org/doi/10.1103/zfk4-rxh1},
doi = {10.1103/zfk4-rxh1},
year = {2025},
date = {2025-12-15},
urldate = {2025-12-15},
journal = {Phys. Rev. B},
volume = {112},
number = {23},
pages = {235140},
abstract = {Van Hove (VH) singularities in the single-particle band spectrum are important for interaction-driven quantum phases. Whereas VH points are usually spin-degenerate, in newly proposed altermagnets VH singularities can become spin-dependent, due to momentum-dependent spin polarization of the Fermi surfaces arising from combined rotation and time-reversal symmetry. We consider two altermagnetic models (𝑑𝑥2−𝑦2- and 𝑑𝑥𝑦-wave) on a square lattice with spin-polarized VH points, and study their stable fixed-point solutions indicating interaction-induced instabilities using parquet renormalization group. For both models, we find new stable fixed-point solutions of the renormalization group equations which are not connected to the solution in the spin-degenerate limit. This implies that on the square lattice, the system with VH singularities is unstable with respect to altermagnetic perturbations. The leading instability for the 𝑑𝑥2−𝑦2 model is real transverse spin density wave. For the 𝑑𝑥𝑦-wave model, it is found to be real transverse spin density wave at large altermagnetic splitting. At small altermagnetic splitting both imaginary charge density wave and real longitudinal spin density waves are dominant.},
note = {datadoi: 10.5281/zenodo.17868124},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Van Hove (VH) singularities in the single-particle band spectrum are important for interaction-driven quantum phases. Whereas VH points are usually spin-degenerate, in newly proposed altermagnets VH singularities can become spin-dependent, due to momentum-dependent spin polarization of the Fermi surfaces arising from combined rotation and time-reversal symmetry. We consider two altermagnetic models (𝑑𝑥2−𝑦2- and 𝑑𝑥𝑦-wave) on a square lattice with spin-polarized VH points, and study their stable fixed-point solutions indicating interaction-induced instabilities using parquet renormalization group. For both models, we find new stable fixed-point solutions of the renormalization group equations which are not connected to the solution in the spin-degenerate limit. This implies that on the square lattice, the system with VH singularities is unstable with respect to altermagnetic perturbations. The leading instability for the 𝑑𝑥2−𝑦2 model is real transverse spin density wave. For the 𝑑𝑥𝑦-wave model, it is found to be real transverse spin density wave at large altermagnetic splitting. At small altermagnetic splitting both imaginary charge density wave and real longitudinal spin density waves are dominant. |  |
Ferrari, F.; Willsher, J.; Seifert, U. F. P.; Valentí, R.; Knolle, J. Stability of algebraic spin liquids coupled to quantum phonons Journal Article Phys. Rev. Res. 7, L042053 (2025), datadoi: 10.5281/zenodo.14039384. @article{ferrariStabilityAlgebraicSpin2025,
title = {Stability of algebraic spin liquids coupled to quantum phonons},
author = {F. Ferrari and J. Willsher and U. F. P. Seifert and R. Valentí and J. Knolle},
url = {https://link.aps.org/doi/10.1103/9wnn-w8bg},
doi = {10.1103/9wnn-w8bg},
year = {2025},
date = {2025-12-05},
urldate = {2025-12-01},
journal = {Phys. Rev. Res.},
volume = {7},
number = {4},
pages = {L042053},
publisher = {American Physical Society},
abstract = {Algebraic spin liquids are quantum disordered phases of insulating magnets that exhibit fractionalized gapless excitations and power-law correlations. Quantum spin liquids in this category include the experimentally established one-dimensional (1D) Luttinger liquid, as well as the U(1) Dirac spin liquid (DSL) that has been a focus of recent candidate materials searches. Most notably, several exchange-frustrated Heisenberg materials on the triangular lattice have shown evidence of the U(1) DSL. In this work, we measure the algebraic correlations of spin-singlet excitations in the 𝐽1−𝐽2 antiferromagnetic Heisenberg model on the triangular lattice, prompting a detailed investigation of this model’s stability under spin-lattice coupling with dynamical quantum phonons using variational Monte Carlo. As seen before in 1D spin chains, we observe a low-temperature transition from a U(1) DSL to valence bond order and predict the parameter regime where the model realizes a stable DSL ground state. To achieve this, we employ a series of finite-size scaling Ansätze inspired by the low-energy DSL’s conformal description in terms of quantum electrodynamics and show that emergent monopole operators drive the instability. We compare the physics of this transition to the 1D Luttinger liquid throughout our analysis. We derive the regime of stability against spin-Peierls ordering and argue that the DSL ground state might still be achievable in candidate materials, despite its tendency to valence bond solid ordering.},
note = {datadoi: 10.5281/zenodo.14039384},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Algebraic spin liquids are quantum disordered phases of insulating magnets that exhibit fractionalized gapless excitations and power-law correlations. Quantum spin liquids in this category include the experimentally established one-dimensional (1D) Luttinger liquid, as well as the U(1) Dirac spin liquid (DSL) that has been a focus of recent candidate materials searches. Most notably, several exchange-frustrated Heisenberg materials on the triangular lattice have shown evidence of the U(1) DSL. In this work, we measure the algebraic correlations of spin-singlet excitations in the 𝐽1−𝐽2 antiferromagnetic Heisenberg model on the triangular lattice, prompting a detailed investigation of this model’s stability under spin-lattice coupling with dynamical quantum phonons using variational Monte Carlo. As seen before in 1D spin chains, we observe a low-temperature transition from a U(1) DSL to valence bond order and predict the parameter regime where the model realizes a stable DSL ground state. To achieve this, we employ a series of finite-size scaling Ansätze inspired by the low-energy DSL’s conformal description in terms of quantum electrodynamics and show that emergent monopole operators drive the instability. We compare the physics of this transition to the 1D Luttinger liquid throughout our analysis. We derive the regime of stability against spin-Peierls ordering and argue that the DSL ground state might still be achievable in candidate materials, despite its tendency to valence bond solid ordering. | |
Wu, Y.; Dai, Z.; Anand, S.; Lin, S. -H.; Yang, Q.; Wang, L.; Pollmann, F.; Zaletel, M. P. Alternating and Gaussian Fermionic Isometric Tensor Network States Journal Article PRX Quantum 6, 040324 (2025). @article{wu_alternating_2025,
title = {Alternating and Gaussian Fermionic Isometric Tensor Network States},
author = {Y. Wu and Z. Dai and S. Anand and S. -H. Lin and Q. Yang and L. Wang and F. Pollmann and M. P. Zaletel},
url = {https://link.aps.org/doi/10.1103/8ypw-c8t4},
doi = {10.1103/8ypw-c8t4},
year = {2025},
date = {2025-11-05},
urldate = {2025-11-01},
journal = {PRX Quantum},
volume = {6},
number = {4},
pages = {040324},
abstract = {Isometric tensor networks in two dimensions enable efficient and accurate study of quantum many-body states, yet the effect of the isometric restriction on the represented quantum states is not fully understood. We address this question in two main contributions. First, we introduce an improved variant of isometric tensor network states (isoTNS) in two dimensions, where the isometric arrows on the columns of the network alternate between pointing upward and downward; hence the name alternating isometric tensor network states. Second, we introduce a numerical tool—the isometric Gaussian fermionic TNS (isoGfTNS)—that incorporates isometric constraints into the framework of Gaussian fermionic tensor network states. We demonstrate in numerous ways that alternating isoTNSs represent many-body ground states of two-dimensional quantum systems significantly better than the original isoTNSs. First, we show that the entanglement in an isoTNS is mediated along the isometric arrows and that alternating isoTNSs mediate entanglement more efficiently than conventional isoTNSs. Second, alternating isoTNSs correspond to a deeper, and thus more representative, sequential-circuit construction of depth 𝒪(𝐿𝑥 ⋅𝐿𝑦) compared to the original isoTNSs of depth 𝒪(𝐿𝑥 +𝐿𝑦). Third, using the Gaussian framework and gradient-based energy minimization, we provide numerical evidence of better bond-dimension scaling and variational energy of alternating isoGfTNSs for ground states of various free-fermionic models, including the Fermi surface, the band insulator, and the 𝑝𝑥 +𝑖𝑝𝑦 mean-field superconductor. Finally, benchmarking on the transverse-field Ising model, we demonstrate that an alternating isoTNS provides substantially improved performance and stability relative to the original isoTNS for the ground-state search algorithm in interacting systems.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Isometric tensor networks in two dimensions enable efficient and accurate study of quantum many-body states, yet the effect of the isometric restriction on the represented quantum states is not fully understood. We address this question in two main contributions. First, we introduce an improved variant of isometric tensor network states (isoTNS) in two dimensions, where the isometric arrows on the columns of the network alternate between pointing upward and downward; hence the name alternating isometric tensor network states. Second, we introduce a numerical tool—the isometric Gaussian fermionic TNS (isoGfTNS)—that incorporates isometric constraints into the framework of Gaussian fermionic tensor network states. We demonstrate in numerous ways that alternating isoTNSs represent many-body ground states of two-dimensional quantum systems significantly better than the original isoTNSs. First, we show that the entanglement in an isoTNS is mediated along the isometric arrows and that alternating isoTNSs mediate entanglement more efficiently than conventional isoTNSs. Second, alternating isoTNSs correspond to a deeper, and thus more representative, sequential-circuit construction of depth 𝒪(𝐿𝑥 ⋅𝐿𝑦) compared to the original isoTNSs of depth 𝒪(𝐿𝑥 +𝐿𝑦). Third, using the Gaussian framework and gradient-based energy minimization, we provide numerical evidence of better bond-dimension scaling and variational energy of alternating isoGfTNSs for ground states of various free-fermionic models, including the Fermi surface, the band insulator, and the 𝑝𝑥 +𝑖𝑝𝑦 mean-field superconductor. Finally, benchmarking on the transverse-field Ising model, we demonstrate that an alternating isoTNS provides substantially improved performance and stability relative to the original isoTNS for the ground-state search algorithm in interacting systems. | |
Rao, P.; Knolle, J. Order-by-disorder in magnets with frustrated spin interactions—classical and large-S limits via the spin functional integral Journal Article J. Phys.: Condens. Matter 37, 405802 (2025). @article{rao_order-by-disorder_2025,
title = {Order-by-disorder in magnets with frustrated spin interactions—classical and large-S limits via the spin functional integral},
author = {P. Rao and J. Knolle},
url = {https://doi.org/10.1088/1361-648X/ae0bdf},
doi = {10.1088/1361-648X/ae0bdf},
year = {2025},
date = {2025-10-07},
urldate = {2025-10-01},
journal = {J. Phys.: Condens. Matter},
volume = {37},
number = {40},
pages = {405802},
abstract = {We investigate spin systems with extensive degeneracies in the classical ground states due to anisotropic frustrated spin interactions, where the degeneracy is not protected by symmetry. Using spin functional integration, we study the lifting of the degeneracies by fluctuations called order-by-disorder (ObD), and the associated gap in the spin-wave spectrum. It is shown that ObD corresponds to gradient-dependent anisotropic interactions of the pseudo-Goldstone modes, which vanish for a classical uniform spin configuration. Fluctuations generate a gradient-independent effective potential which determines the ground state and the pseudo-Goldstone gap. Furthermore, we recover previous predictions for the pseudo-Goldstone gap in type-I and II ObD with two-spin interactions in the large spin-S limit or the classical small temperature limit, by computing the gap explicitly for the type-II cubic compass model and the type-I square compass model. We show that these two limits correspond to the one-loop approximation for the effective potential. We also discuss other types of order by disorder due to m-spin interactions where m > 2.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We investigate spin systems with extensive degeneracies in the classical ground states due to anisotropic frustrated spin interactions, where the degeneracy is not protected by symmetry. Using spin functional integration, we study the lifting of the degeneracies by fluctuations called order-by-disorder (ObD), and the associated gap in the spin-wave spectrum. It is shown that ObD corresponds to gradient-dependent anisotropic interactions of the pseudo-Goldstone modes, which vanish for a classical uniform spin configuration. Fluctuations generate a gradient-independent effective potential which determines the ground state and the pseudo-Goldstone gap. Furthermore, we recover previous predictions for the pseudo-Goldstone gap in type-I and II ObD with two-spin interactions in the large spin-S limit or the classical small temperature limit, by computing the gap explicitly for the type-II cubic compass model and the type-I square compass model. We show that these two limits correspond to the one-loop approximation for the effective potential. We also discuss other types of order by disorder due to m-spin interactions where m > 2. | |
Birnkammer, S.; Knap, M.; Knolle, J.; Mook, A.; Bastianello, A. Scattering theory of chiral edge modes in topological magnon insulators Journal Article Phys. Rev. B 112, 094417 (2025), datadoi: 10.5281/zenodo.13895647. @article{birnkammerScatteringTheoryChiral2025,
title = {Scattering theory of chiral edge modes in topological magnon insulators},
author = {S. Birnkammer and M. Knap and J. Knolle and A. Mook and A. Bastianello},
url = {https://link.aps.org/doi/10.1103/btt2-mp62},
doi = {10.1103/btt2-mp62},
year = {2025},
date = {2025-09-09},
urldate = {2025-09-09},
journal = {Phys. Rev. B},
volume = {112},
number = {9},
pages = {094417},
abstract = {Topological magnon insulators exhibit robust edge modes with chiral properties similar to quantum Hall edge states. However, due to their strong localization at the edges, interactions between these chiral edge magnons can be significant, as we show in a model of coupled magnon-conserving spin chains in an electric field gradient. The chiral edge modes remain edge-localized and do not scatter into the bulk, and we characterize their scattering phase: for strongly localized edge modes, we observe significant deviation from the bare scattering phase. This renormalization of edge scattering can be attributed to bound bulk modes resonating with the chiral edge magnons in the spirit of Feshbach resonances in atomic physics. We argue that the scattering dynamics can be probed experimentally with a real-time measurement protocol using inelastic scanning tunneling spectroscopy. Our results show that interaction among magnons can be encoded in an effective edge model of reduced dimensionality, where the interactions with the bulk renormalize the effective couplings. Our work introduces a systematic way to determine the many-body effective theory for edge states in topological magnon insulators.},
note = {datadoi: 10.5281/zenodo.13895647},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Topological magnon insulators exhibit robust edge modes with chiral properties similar to quantum Hall edge states. However, due to their strong localization at the edges, interactions between these chiral edge magnons can be significant, as we show in a model of coupled magnon-conserving spin chains in an electric field gradient. The chiral edge modes remain edge-localized and do not scatter into the bulk, and we characterize their scattering phase: for strongly localized edge modes, we observe significant deviation from the bare scattering phase. This renormalization of edge scattering can be attributed to bound bulk modes resonating with the chiral edge magnons in the spirit of Feshbach resonances in atomic physics. We argue that the scattering dynamics can be probed experimentally with a real-time measurement protocol using inelastic scanning tunneling spectroscopy. Our results show that interaction among magnons can be encoded in an effective edge model of reduced dimensionality, where the interactions with the bulk renormalize the effective couplings. Our work introduces a systematic way to determine the many-body effective theory for edge states in topological magnon insulators. | |
Rao, P.; Moessner, R.; Knolle, J. Dynamical response theory of interacting Majorana fermions and its application to generic Kitaev quantum spin liquids in a field Journal Article Phys. Rev. B 112, 024440 (2025), datadoi: (10.5281/zenodo.15125435). @article{raoDynamicalResponseTheory2025,
title = {Dynamical response theory of interacting Majorana fermions and its application to generic Kitaev quantum spin liquids in a field},
author = {P. Rao and R. Moessner and J. Knolle},
url = {https://link.aps.org/doi/10.1103/f4b4-h1yr},
doi = {10.1103/f4b4-h1yr},
year = {2025},
date = {2025-07-28},
urldate = {2025-07-01},
journal = {Phys. Rev. B},
volume = {112},
number = {2},
pages = {024440},
abstract = {Motivated by the appearance of Majorana fermions in a broad range of correlated and topological electronic systems, we develop a general method to compute the dynamical response of interacting Majorana fermions in the random-phase approximation (RPA). This can be applied self-consistently on top of Majorana mean-field theory backgrounds, thereby in particular providing a powerful tool to analyze generic behavior in the vicinity of (various heavily studied) exactly soluble models. Prime examples are quantum spin liquids (QSL) with emergent Majorana excitations, with the celebrated exact solution of Kitaev. We employ the RPA to study in considerable detail phase structure and dynamics of the extended Kitaev honeycomb 𝐾𝐽Γ model, with and without an applied field. First, we benchmark our method with Kitaev's exactly soluble model, finding a remarkable agreement. The interactions between Majorana fermions even turn out to mimic the effect of local ℤ2 flux excitations, which we explain analytically. Second, we show how small non-Kitaev couplings 𝐽 and Γ induce Majorana bound states, resulting in sharp features in the dynamical structure factor in the presence of fractionalization: such “spinon excitons” naturally appear, and can coexist and interact with the broad Majorana continuum. Third, for increasing couplings or field, our theory predicts instabilities of the Kitaev QSL (KQSL) triggered by the condensation of the sharp modes. From the high-symmetry momenta of the condensation we can deduce which magnetically ordered phases surround the KQSL, in good agreement with previous finite-size numerics. We discuss implications for experiments and the broad range of applicability of our method to other QSL and Majorana systems.},
note = {datadoi: (10.5281/zenodo.15125435)},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Motivated by the appearance of Majorana fermions in a broad range of correlated and topological electronic systems, we develop a general method to compute the dynamical response of interacting Majorana fermions in the random-phase approximation (RPA). This can be applied self-consistently on top of Majorana mean-field theory backgrounds, thereby in particular providing a powerful tool to analyze generic behavior in the vicinity of (various heavily studied) exactly soluble models. Prime examples are quantum spin liquids (QSL) with emergent Majorana excitations, with the celebrated exact solution of Kitaev. We employ the RPA to study in considerable detail phase structure and dynamics of the extended Kitaev honeycomb 𝐾𝐽Γ model, with and without an applied field. First, we benchmark our method with Kitaev's exactly soluble model, finding a remarkable agreement. The interactions between Majorana fermions even turn out to mimic the effect of local ℤ2 flux excitations, which we explain analytically. Second, we show how small non-Kitaev couplings 𝐽 and Γ induce Majorana bound states, resulting in sharp features in the dynamical structure factor in the presence of fractionalization: such “spinon excitons” naturally appear, and can coexist and interact with the broad Majorana continuum. Third, for increasing couplings or field, our theory predicts instabilities of the Kitaev QSL (KQSL) triggered by the condensation of the sharp modes. From the high-symmetry momenta of the condensation we can deduce which magnetically ordered phases surround the KQSL, in good agreement with previous finite-size numerics. We discuss implications for experiments and the broad range of applicability of our method to other QSL and Majorana systems. | |
Natori, W.; Yang, Y.; Jin, H. -K.; Knolle, J.; Perkins, N. B. Ferrimagnetic Kitaev spin liquids in mixed spin-1/2 and spin-3/2 honeycomb magnets Journal Article Phys. Rev. B 111, 214411 (2025). @article{natori_ferrimagnetic_2025,
title = {Ferrimagnetic Kitaev spin liquids in mixed spin-1/2 and spin-3/2 honeycomb magnets},
author = {W. Natori and Y. Yang and H. -K. Jin and J. Knolle and N. B. Perkins},
url = {https://link.aps.org/doi/10.1103/PhysRevB.111.214411},
doi = {10.1103/PhysRevB.111.214411},
year = {2025},
date = {2025-06-04},
urldate = {2025-06-01},
journal = {Phys. Rev. B},
volume = {111},
number = {21},
pages = {214411},
abstract = {We explore the phase diagram of a mixed-spin Kitaev model, where spin-1/2 and spin-3/2 ions form a staggered pattern on a honeycomb lattice. Enabled by an exact mapping of local conserved flux operators onto 𝑍2 gauge fields, we perform a parton mean-field theory for the model with a single-ion anisotropy. The phase diagram contains four types of quantum spin liquids distinguished by quadrupolar parameters. These analytical results are quantitatively confirmed by state-of-the-art DMRG simulations. We also explore the potential experimental realization of the mixed-spin Kitaev model in materials such as Zr0.5Ru0.5Cl3. By developing a superexchange theory specifically for this mixed-spin system, we identify the conditions under which dominant Kitaev-like interactions emerge. Our findings highlight the importance of spin-orbital couplings and quadrupolar order parameters in stabilizing exotic phases, providing a foundation for exploring mixed-spin Kitaev magnets.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We explore the phase diagram of a mixed-spin Kitaev model, where spin-1/2 and spin-3/2 ions form a staggered pattern on a honeycomb lattice. Enabled by an exact mapping of local conserved flux operators onto 𝑍2 gauge fields, we perform a parton mean-field theory for the model with a single-ion anisotropy. The phase diagram contains four types of quantum spin liquids distinguished by quadrupolar parameters. These analytical results are quantitatively confirmed by state-of-the-art DMRG simulations. We also explore the potential experimental realization of the mixed-spin Kitaev model in materials such as Zr0.5Ru0.5Cl3. By developing a superexchange theory specifically for this mixed-spin system, we identify the conditions under which dominant Kitaev-like interactions emerge. Our findings highlight the importance of spin-orbital couplings and quadrupolar order parameters in stabilizing exotic phases, providing a foundation for exploring mixed-spin Kitaev magnets. | |
Xu, W. -T.; Pollmann, F.; Knap, M. Critical behavior of Fredenhagen-Marcu string order parameters at topological phase transitions with emergent higher-form symmetries Journal Article npj Quantum Inf. 11, 74 (2025), datadoi: (10.5281/zenodo.10494399). @article{xuCriticalBehaviorFredenhagenMarcu2025,
title = {Critical behavior of Fredenhagen-Marcu string order parameters at topological phase transitions with emergent higher-form symmetries},
author = {W. -T. Xu and F. Pollmann and M. Knap},
url = {https://doi.org/10.1038/s41534-025-01030-z},
doi = {10.1038/s41534-025-01030-z},
year = {2025},
date = {2025-05-09},
urldate = {2025-05-09},
journal = {npj Quantum Inf.},
volume = {11},
number = {1},
pages = {74},
abstract = {A nonlocal string order parameter detecting topological order and deconfinement has been proposed by Fredenhagen and Marcu (FM). However, due to the lack of exact internal symmetries for lattice models and the nonlinear dependence of the FM string order parameter on ground states, it is a priori not guaranteed that it is a genuine order parameter for topological phase transitions. In this work, we find that the FM string order parameter exhibits universal scaling behavior near critical points of charge condensation transitions, by directly evaluating the FM string order parameter in the infinite string-length limit using infinite Projected Entangled Pair States (iPEPS) for the toric code in a magnetic field. Our results thus demonstrate that the FM string order parameter represents a quantitatively well-behaved order parameter. We find that only in the presence of an emergent 1-form symmetry the corresponding FM string order parameter can faithfully detect topological transitions.},
note = {datadoi: (10.5281/zenodo.10494399)},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
A nonlocal string order parameter detecting topological order and deconfinement has been proposed by Fredenhagen and Marcu (FM). However, due to the lack of exact internal symmetries for lattice models and the nonlinear dependence of the FM string order parameter on ground states, it is a priori not guaranteed that it is a genuine order parameter for topological phase transitions. In this work, we find that the FM string order parameter exhibits universal scaling behavior near critical points of charge condensation transitions, by directly evaluating the FM string order parameter in the infinite string-length limit using infinite Projected Entangled Pair States (iPEPS) for the toric code in a magnetic field. Our results thus demonstrate that the FM string order parameter represents a quantitatively well-behaved order parameter. We find that only in the presence of an emergent 1-form symmetry the corresponding FM string order parameter can faithfully detect topological transitions. | |
Mangeolle, L.; Knolle, J. Anomalous Quantum Oscillations from Boson-Mediated Interband Scattering Journal Article Phys. Rev. Lett. 134, 146502 (2025). @article{mangeolle_anomalous_2025-1,
title = {Anomalous Quantum Oscillations from Boson-Mediated Interband Scattering},
author = {L. Mangeolle and J. Knolle},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.134.146502},
doi = {10.1103/PhysRevLett.134.146502},
year = {2025},
date = {2025-04-09},
urldate = {2025-04-01},
journal = {Phys. Rev. Lett.},
volume = {134},
number = {14},
pages = {146502},
abstract = {Quantum oscillations (QOs) in metals refer to the periodic variation of thermodynamic and transport properties as a function of inverse applied magnetic field. QO frequencies are normally associated with semiclassical trajectories of Fermi surface orbits, but recent experiments challenge the canonical description. We develop a theory of composite frequency quantum oscillations (CFQOs) in two-dimensional Fermi liquids with several Fermi surfaces and interband scattering mediated by a dynamical boson, e.g., phonons or spin fluctuations. Specifically, we show that CFQOs arise from oscillations in the fermionic self-energy with anomalous frequency splitting and distinct strongly non-Lifshitz–Kosevich temperature dependences. Our theory goes beyond the framework of semiclassical Fermi surface trajectories highlighting the role of interaction effects. We provide experimental predictions and discuss the effect of nonequilibrium boson occupation in driven systems.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Quantum oscillations (QOs) in metals refer to the periodic variation of thermodynamic and transport properties as a function of inverse applied magnetic field. QO frequencies are normally associated with semiclassical trajectories of Fermi surface orbits, but recent experiments challenge the canonical description. We develop a theory of composite frequency quantum oscillations (CFQOs) in two-dimensional Fermi liquids with several Fermi surfaces and interband scattering mediated by a dynamical boson, e.g., phonons or spin fluctuations. Specifically, we show that CFQOs arise from oscillations in the fermionic self-energy with anomalous frequency splitting and distinct strongly non-Lifshitz–Kosevich temperature dependences. Our theory goes beyond the framework of semiclassical Fermi surface trajectories highlighting the role of interaction effects. We provide experimental predictions and discuss the effect of nonequilibrium boson occupation in driven systems. | |
Xu, W. -T.; Rakovszky, T.; Knap, M.; Pollmann, F. Entanglement Properties of Gauge Theories from Higher-Form Symmetries Journal Article Phys. Rev. X 15, 011001 (2025), datadoi: (10.5281/zenodo.14360829). @article{xuEntanglementPropertiesGauge2025,
title = {Entanglement Properties of Gauge Theories from Higher-Form Symmetries},
author = {W. -T. Xu and T. Rakovszky and M. Knap and F. Pollmann},
doi = {10.1103/PhysRevX.15.011001},
year = {2025},
date = {2025-01-02},
urldate = {2025-01-02},
journal = {Phys. Rev. X},
volume = {15},
number = {1},
pages = {011001},
abstract = {We explore the relationship between higher-form symmetries and entanglement properties in lattice gauge theories with discrete gauge groups, which can exhibit both topologically ordered phases and higher-form symmetry-protected topological (SPT) phases. Our study centers on a generalization of the Fradkin-Shenker model describing ℤ2 lattice gauge theory with matter, where the Gauss law constraint can be either emergent or exact. The phase diagram includes a topologically ordered deconfined phase and a nontrivial SPT phase protected by a 1-form and a 0-form symmetry, among others. We obtain the following key findings: First, the entanglement properties of the model depend on whether the 1-form symmetries and the Gauss law constraint are exact or emergent. For the emergent Gauss law, the entanglement spectrum (ES) of the nontrivial SPT phase exhibits degeneracies, which are robust at low energies against weak perturbations that explicitly break the exact 1-form symmetry. When the Gauss law and the 1-form symmetry are both exact, the ES degeneracy is extensive. This extensive degeneracy turns out to be fragile and can be removed completely by infinitesimal perturbations that explicitly break the exact 1-form symmetry while keeping the Gauss law exact. Second, we consider the ES in the topologically ordered phase where 1-form symmetries are spontaneously broken. In contrast to the ES of the nontrivial SPT phase, we find that spontaneous higher-form symmetry breaking removes “half” of the ES levels, leading to a nondegenerate ES in the topologically ordered phase, in general. Third, we derive a connection between spontaneous higher-form symmetry breaking and the topological entanglement entropy (TEE). Using this relation, we investigate the entanglement entropy that can be distilled in the deconfined phase of the original Fradkin-Shenker model using gauge-invariant measurements. We show that the TEE is robust against the measurement when the 1-form symmetry is emergent but it is fragile when the 1-form symmetry is exact. Our results demonstrate the advantage of higher-form symmetries for understanding entanglement properties of gauge theories.},
note = {datadoi: (10.5281/zenodo.14360829)},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We explore the relationship between higher-form symmetries and entanglement properties in lattice gauge theories with discrete gauge groups, which can exhibit both topologically ordered phases and higher-form symmetry-protected topological (SPT) phases. Our study centers on a generalization of the Fradkin-Shenker model describing ℤ2 lattice gauge theory with matter, where the Gauss law constraint can be either emergent or exact. The phase diagram includes a topologically ordered deconfined phase and a nontrivial SPT phase protected by a 1-form and a 0-form symmetry, among others. We obtain the following key findings: First, the entanglement properties of the model depend on whether the 1-form symmetries and the Gauss law constraint are exact or emergent. For the emergent Gauss law, the entanglement spectrum (ES) of the nontrivial SPT phase exhibits degeneracies, which are robust at low energies against weak perturbations that explicitly break the exact 1-form symmetry. When the Gauss law and the 1-form symmetry are both exact, the ES degeneracy is extensive. This extensive degeneracy turns out to be fragile and can be removed completely by infinitesimal perturbations that explicitly break the exact 1-form symmetry while keeping the Gauss law exact. Second, we consider the ES in the topologically ordered phase where 1-form symmetries are spontaneously broken. In contrast to the ES of the nontrivial SPT phase, we find that spontaneous higher-form symmetry breaking removes “half” of the ES levels, leading to a nondegenerate ES in the topologically ordered phase, in general. Third, we derive a connection between spontaneous higher-form symmetry breaking and the topological entanglement entropy (TEE). Using this relation, we investigate the entanglement entropy that can be distilled in the deconfined phase of the original Fradkin-Shenker model using gauge-invariant measurements. We show that the TEE is robust against the measurement when the 1-form symmetry is emergent but it is fragile when the 1-form symmetry is exact. Our results demonstrate the advantage of higher-form symmetries for understanding entanglement properties of gauge theories. | |
2024
|
Hofmeier, D.; Willsher, J.; Seifert, U. F. P.; Knolle, J. Spin-Peierls instability of deconfined quantum critical points Journal Article Phys. Rev. B 110, 125130 (2024). @article{hofmeier_spin-peierls_2024,
title = {Spin-Peierls instability of deconfined quantum critical points},
author = {D. Hofmeier and J. Willsher and U. F. P. Seifert and J. Knolle},
url = {https://link.aps.org/doi/10.1103/PhysRevB.110.125130},
doi = {10.1103/PhysRevB.110.125130},
year = {2024},
date = {2024-09-13},
urldate = {2024-09-01},
journal = {Phys. Rev. B},
volume = {110},
number = {12},
pages = {125130},
abstract = {Deconfined quantum critical points (DQCPs) are putative phase transitions beyond the Landau paradigm with emergent fractionalized degrees of freedom. The original example of a DQCP is the spin-1/2 quantum antiferromagnet on the square lattice which features a second-order transition between valence bond solid (VBS) and Néel order. The VBS order breaks a lattice symmetry, and the corresponding VBS order parameter may couple to lattice distortion modes (phonons) at appropriate momenta. We investigate a field-theoretic description of the DQCP in the presence of such a spin-lattice coupling. We show that treating phonons as classical lattice distortions leads to a relevant monopole-phonon interaction inducing an instability towards a distorted lattice by an analogous mechanism to the spin-Peierls instability in one dimension. Consequently, there is a breakdown of the DQCP which generally becomes a strong first-order transition. Taking into account the full quantum nature of the phonons, we argue that the continuous DQCP persists above a critical phonon frequency. Lastly, we comment on the connection to general gapless, deconfined gauge theories.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Deconfined quantum critical points (DQCPs) are putative phase transitions beyond the Landau paradigm with emergent fractionalized degrees of freedom. The original example of a DQCP is the spin-1/2 quantum antiferromagnet on the square lattice which features a second-order transition between valence bond solid (VBS) and Néel order. The VBS order breaks a lattice symmetry, and the corresponding VBS order parameter may couple to lattice distortion modes (phonons) at appropriate momenta. We investigate a field-theoretic description of the DQCP in the presence of such a spin-lattice coupling. We show that treating phonons as classical lattice distortions leads to a relevant monopole-phonon interaction inducing an instability towards a distorted lattice by an analogous mechanism to the spin-Peierls instability in one dimension. Consequently, there is a breakdown of the DQCP which generally becomes a strong first-order transition. Taking into account the full quantum nature of the phonons, we argue that the continuous DQCP persists above a critical phonon frequency. Lastly, we comment on the connection to general gapless, deconfined gauge theories. | |
Kirchner, N.; Choi, W.; Pollmann, F. Characterizing the entanglement of anyonic systems using the anyonic partial transpose Journal Article Phys. Rev. B 110, 085143 (2024), datadoi: 10.5281/zenodo.10825841. @article{kirchnerCharacterizingEntanglementAnyonic2024,
title = {Characterizing the entanglement of anyonic systems using the anyonic partial transpose},
author = {N. Kirchner and W. Choi and F. Pollmann},
doi = {10.1103/PhysRevB.110.085143},
year = {2024},
date = {2024-08-21},
urldate = {2024-08-01},
journal = {Phys. Rev. B},
volume = {110},
number = {8},
pages = {085143},
abstract = {Entanglement of mixed quantum states can be quantified using the partial transpose and its corresponding entanglement measure, the logarithmic negativity. Recently, the notion of partial transpose has been extended to systems of anyons, which are exotic quasiparticles whose exchange statistics go beyond the bosonic and fermionic cases. Studying the fundamental properties of this anyonic partial transpose, we first reveal that when applied to the special case of fermionic systems, it can be reduced to the fermionic partial transpose or its twisted variant depending on whether or not a boundary Majorana fermion is present. Focusing on ground state properties, we find that the anyonic partial transpose captures both the correct entanglement scaling for gapless systems, as predicted by conformal field theory, and the phase transition between a topologically trivial and a nontrivial phase. For non-Abelian anyons and the bipartition geometry, we find a rich multiplet structure in the eigenvalues of the partial transpose, the so-called negativity spectrum, and reveal the possibility of defining both a charge- and an imbalance-resolved negativity.},
note = {datadoi: 10.5281/zenodo.10825841},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Entanglement of mixed quantum states can be quantified using the partial transpose and its corresponding entanglement measure, the logarithmic negativity. Recently, the notion of partial transpose has been extended to systems of anyons, which are exotic quasiparticles whose exchange statistics go beyond the bosonic and fermionic cases. Studying the fundamental properties of this anyonic partial transpose, we first reveal that when applied to the special case of fermionic systems, it can be reduced to the fermionic partial transpose or its twisted variant depending on whether or not a boundary Majorana fermion is present. Focusing on ground state properties, we find that the anyonic partial transpose captures both the correct entanglement scaling for gapless systems, as predicted by conformal field theory, and the phase transition between a topologically trivial and a nontrivial phase. For non-Abelian anyons and the bipartition geometry, we find a rich multiplet structure in the eigenvalues of the partial transpose, the so-called negativity spectrum, and reveal the possibility of defining both a charge- and an imbalance-resolved negativity. | |
Seifert, U. F. P.; Willsher, J.; Drescher, M.; Pollmann, F.; Knolle, J. Spin-Peierls instability of the U(1) Dirac spin liquid Journal Article Nat. Commun. 15, 7110 (2024), datadoi: 10.5281/zenodo.8246416. @article{seifertSpinPeierlsInstabilityU12024,
title = {Spin-Peierls instability of the U(1) Dirac spin liquid},
author = {U. F. P. Seifert and J. Willsher and M. Drescher and F. Pollmann and J. Knolle},
url = {https://doi.org/10.1038/s41467-024-51367-w},
doi = {10.1038/s41467-024-51367-w},
year = {2024},
date = {2024-08-19},
urldate = {2024-08-01},
journal = {Nat. Commun.},
volume = {15},
number = {1},
pages = {7110},
abstract = {Quantum fluctuations can inhibit long-range ordering in frustrated magnets and potentially lead to quantum spin liquid (QSL) phases. A prime example are gapless QSLs with emergent U(1) gauge fields, which have been understood to be described in terms of quantum electrodynamics in 2+1 dimension (QED3). Despite several promising candidate materials, however, a complicating factor for their realisation is the presence of other degrees of freedom. In particular lattice distortions can act to relieve magnetic frustration, precipitating conventionally ordered states. In this work, we use field-theoretic arguments as well as extensive numerical simulations to show that the U(1) Dirac QSL on the triangular and kagome lattices exhibits a weak-coupling instability due to the coupling of monopoles of the emergent gauge field to lattice distortions, leading to valence-bond solid ordering. This generalises the spin-Peierls instability of one-dimensional quantum critical spin chains to two-dimensional algebraic QSLs. We study static distortions as well as quantum-mechanical phonons. Even in regimes where the QSL is stable, the singular spin-lattice coupling leads to marked temperature-dependent corrections to the phonon spectrum, which provide salient experimental signatures of spin fractionalisation. We discuss the coupling of QSLs to the lattice as a general tool for their discovery and characterisation.},
note = {datadoi: 10.5281/zenodo.8246416},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Quantum fluctuations can inhibit long-range ordering in frustrated magnets and potentially lead to quantum spin liquid (QSL) phases. A prime example are gapless QSLs with emergent U(1) gauge fields, which have been understood to be described in terms of quantum electrodynamics in 2+1 dimension (QED3). Despite several promising candidate materials, however, a complicating factor for their realisation is the presence of other degrees of freedom. In particular lattice distortions can act to relieve magnetic frustration, precipitating conventionally ordered states. In this work, we use field-theoretic arguments as well as extensive numerical simulations to show that the U(1) Dirac QSL on the triangular and kagome lattices exhibits a weak-coupling instability due to the coupling of monopoles of the emergent gauge field to lattice distortions, leading to valence-bond solid ordering. This generalises the spin-Peierls instability of one-dimensional quantum critical spin chains to two-dimensional algebraic QSLs. We study static distortions as well as quantum-mechanical phonons. Even in regimes where the QSL is stable, the singular spin-lattice coupling leads to marked temperature-dependent corrections to the phonon spectrum, which provide salient experimental signatures of spin fractionalisation. We discuss the coupling of QSLs to the lattice as a general tool for their discovery and characterisation. | |
Chen, A.; Heyl, M. Empowering deep neural quantum states through efficient optimization Journal Article Nat. Phys. 20, 1476 (2024), datadoi: (10.5281/zenodo.7657551). @article{chenEmpoweringDeepNeural2024,
title = {Empowering deep neural quantum states through efficient optimization},
author = {A. Chen and M. Heyl},
url = {https://doi.org/10.1038/s41567-024-02566-1},
doi = {10.1038/s41567-024-02566-1},
year = {2024},
date = {2024-07-01},
urldate = {2024-07-01},
journal = {Nat. Phys.},
volume = {20},
number = {9},
pages = {1476},
abstract = {Computing the ground state of interacting quantum matter is a long-standing challenge, especially for complex two-dimensional systems. Recent developments have highlighted the potential of neural quantum states to solve the quantum many-body problem by encoding the many-body wavefunction into artificial neural networks. However, this method has faced the critical limitation that existing optimization algorithms are not suitable for training modern large-scale deep network architectures. Here, we introduce a minimum-step stochastic-reconfiguration optimization algorithm, which allows us to train deep neural quantum states with up to 106 parameters. We demonstrate our method for paradigmatic frustrated spin-1/2 models on square and triangular lattices, for which our trained deep networks approach machine precision and yield improved variational energies compared to existing results. Equipped with our optimization algorithm, we find numerical evidence for gapless quantum-spin-liquid phases in the considered models, an open question to date. We present a method that captures the emergent complexity in quantum many-body problems through the expressive power of large-scale artificial neural networks.},
note = {datadoi: (10.5281/zenodo.7657551)},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Computing the ground state of interacting quantum matter is a long-standing challenge, especially for complex two-dimensional systems. Recent developments have highlighted the potential of neural quantum states to solve the quantum many-body problem by encoding the many-body wavefunction into artificial neural networks. However, this method has faced the critical limitation that existing optimization algorithms are not suitable for training modern large-scale deep network architectures. Here, we introduce a minimum-step stochastic-reconfiguration optimization algorithm, which allows us to train deep neural quantum states with up to 106 parameters. We demonstrate our method for paradigmatic frustrated spin-1/2 models on square and triangular lattices, for which our trained deep networks approach machine precision and yield improved variational energies compared to existing results. Equipped with our optimization algorithm, we find numerical evidence for gapless quantum-spin-liquid phases in the considered models, an open question to date. We present a method that captures the emergent complexity in quantum many-body problems through the expressive power of large-scale artificial neural networks. | |
Kosior, A.; Heyl, M. Vortex loop dynamics and dynamical quantum phase transitions in three-dimensional fermion matter Journal Article Phys. Rev. B 109, L140303 (2024), datadoi: (10.5281/zenodo.10837585). @article{kosiorVortexLoopDynamics2024,
title = {Vortex loop dynamics and dynamical quantum phase transitions in three-dimensional fermion matter},
author = {A. Kosior and M. Heyl},
url = {https://doi.org/10.1103/PhysRevB.109.L140303},
doi = {10.1103/physrevb.109.l140303},
year = {2024},
date = {2024-04-15},
urldate = {2024-04-01},
journal = {Phys. Rev. B},
volume = {109},
number = {14},
pages = {L140303},
abstract = {Over the past decade, dynamical quantum phase transitions (DQPTs) have emerged as a paradigm shift in understanding nonequilibrium quantum many-body systems. However, the challenge lies in identifying order parameters that effectively characterize the associated dynamic phases. In this study we investigate the behavior of vortex singularities in the phase of the Green's function for a broad class of fermion lattice models in three dimensions after an instantaneous quench in both interacting and noninteracting systems. We find that the full set of vortices form one-dimensional dynamical objects, which we call vortex loops. We propose that the number of such vortex loops can be interpreted as a quantized order parameter that distinguishes between different nonequilibrium phases. Our results establish an explicit link between variations in the order parameter and DQPTs in the noninteracting scenario. Moreover, we show that the vortex loops are robust in the weakly interacting case, even though there is no direct relation between the Loschmidt amplitude and the Green's function. Finally, we observe that vortex loops can form complex dynamical patterns in momentum space. Our findings provide valuable insights for developing definitions of dynamical order parameters in nonequilibrium systems.},
note = {datadoi: (10.5281/zenodo.10837585)},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Over the past decade, dynamical quantum phase transitions (DQPTs) have emerged as a paradigm shift in understanding nonequilibrium quantum many-body systems. However, the challenge lies in identifying order parameters that effectively characterize the associated dynamic phases. In this study we investigate the behavior of vortex singularities in the phase of the Green's function for a broad class of fermion lattice models in three dimensions after an instantaneous quench in both interacting and noninteracting systems. We find that the full set of vortices form one-dimensional dynamical objects, which we call vortex loops. We propose that the number of such vortex loops can be interpreted as a quantized order parameter that distinguishes between different nonequilibrium phases. Our results establish an explicit link between variations in the order parameter and DQPTs in the noninteracting scenario. Moreover, we show that the vortex loops are robust in the weakly interacting case, even though there is no direct relation between the Loschmidt amplitude and the Green's function. Finally, we observe that vortex loops can form complex dynamical patterns in momentum space. Our findings provide valuable insights for developing definitions of dynamical order parameters in nonequilibrium systems. | |
Kadow, W.; Jin, H. -K.; Knolle, J.; Knap, M. Single-hole spectra of Kitaev spin liquids: From dynamical Nagaoka ferromagnetism to spin-hole fractionalization Journal Article npj Quantum Mater. 9, 32 (2024), datadoi: 10.5281/zenodo.8363616. @article{kadowSingleholeSpectraKitaev2024,
title = {Single-hole spectra of Kitaev spin liquids: From dynamical Nagaoka ferromagnetism to spin-hole fractionalization},
author = {W. Kadow and H. -K. Jin and J. Knolle and M. Knap},
url = {https://doi.org/10.1038/s41535-024-00641-7},
doi = {10.1038/s41535-024-00641-7},
year = {2024},
date = {2024-03-21},
urldate = {2024-03-21},
journal = {npj Quantum Mater.},
volume = {9},
number = {1},
pages = {32},
note = {datadoi: 10.5281/zenodo.8363616},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
| |
2023
|
Huber, N.; Leeb, V.; Bauer, A.; Benka, G.; Knolle, J.; Pfleiderer, C.; Wilde, M. A. Quantum oscillations of the quasiparticle lifetime in a metal Journal Article Nature 621, 276 (2023), datadoi: 10.5281/zenodo.7957066. @article{huberQuantumOscillationsQuasiparticle2023,
title = {Quantum oscillations of the quasiparticle lifetime in a metal},
author = {N. Huber and V. Leeb and A. Bauer and G. Benka and J. Knolle and C. Pfleiderer and M. A. Wilde},
url = {https://doi.org/10.1038/s41586-023-06330-y},
doi = {10.1038/s41586-023-06330-y},
issn = {0028-0836},
year = {2023},
date = {2023-08-02},
urldate = {2023-08-02},
journal = {Nature},
volume = {621},
pages = {276},
abstract = {Following nearly a century of research, it remains a puzzle that the low-lying excitations of metals are remarkably well explained by effective single-particle theories of non-interacting bands(1-4). The abundance of interactions in real materials raises the question of direct spectroscopic signatures of phenomena beyond effective single-particle, single-band behaviour. Here we report the identification of quantum oscillations (QOs) in the three-dimensional topological semimetal CoSi, which defy the standard description in two fundamental aspects. First, the oscillation frequency corresponds to the difference of semiclassical quasiparticle (QP) orbits of two bands, which are forbidden as half of the trajectory would oppose the Lorentz force. Second, the oscillations exist up to above 50 K, in strong contrast to all other oscillatory components, which vanish below a few kelvin. Our findings are in excellent agreement with generic model calculations of QOs of the QP lifetime (QPL). Because the only precondition for their existence is a nonlinear coupling of at least two electronic orbits, for example, owing to QP scattering on defects or collective excitations, such QOs of the QPL are generic for any metal featuring Landau quantization with several orbits. They are consistent with certain frequencies in topological semimetals(5-9), unconventional superconductors(10,11), rare-earth compounds(12-14) and Rashba systems(15), and permit to identify and gauge correlation phenomena, for example, in two-dimensional materials(16,17) and multiband metals(18).},
note = {datadoi: 10.5281/zenodo.7957066},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Following nearly a century of research, it remains a puzzle that the low-lying excitations of metals are remarkably well explained by effective single-particle theories of non-interacting bands(1-4). The abundance of interactions in real materials raises the question of direct spectroscopic signatures of phenomena beyond effective single-particle, single-band behaviour. Here we report the identification of quantum oscillations (QOs) in the three-dimensional topological semimetal CoSi, which defy the standard description in two fundamental aspects. First, the oscillation frequency corresponds to the difference of semiclassical quasiparticle (QP) orbits of two bands, which are forbidden as half of the trajectory would oppose the Lorentz force. Second, the oscillations exist up to above 50 K, in strong contrast to all other oscillatory components, which vanish below a few kelvin. Our findings are in excellent agreement with generic model calculations of QOs of the QP lifetime (QPL). Because the only precondition for their existence is a nonlinear coupling of at least two electronic orbits, for example, owing to QP scattering on defects or collective excitations, such QOs of the QPL are generic for any metal featuring Landau quantization with several orbits. They are consistent with certain frequencies in topological semimetals(5-9), unconventional superconductors(10,11), rare-earth compounds(12-14) and Rashba systems(15), and permit to identify and gauge correlation phenomena, for example, in two-dimensional materials(16,17) and multiband metals(18). | |
