@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}

}

@article{birnkammer_scattering_2025,

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 = {2025-09-01},

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.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{rao_dynamical_2025,

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 𝐾⁢𝐽⁢Γ 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.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@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 Zr0.5⁢Ru0.5⁢Cl3. 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}

}

@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}

}

@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}

}

@article{seifert_spin-peierls_2024,

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.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{chen_empowering_2024,

title = {Empowering deep neural quantum states through efficient optimization},

author = {A. Chen and M. Heyl},

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.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{kosior_vortex_2024,

title = {Vortex loop dynamics and dynamical quantum phase transitions in three-dimensional fermion matter},

author = {A. Kosior and M. Heyl},

doi = {10.1103/physrevb.109.l140303},

year  = {2024},

date = {2024-04-15},

urldate = {2024-01-01},

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.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{kadow_single-hole_2024,

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 = {2024-03-01},

urldate = {2024-03-01},

journal = {npj Quantum Mater.},

volume = {9},

number = {1},

pages = {32},

abstract = {The dynamical response of a quantum spin liquid upon injecting a hole is a pertinent open question. In experiments, the hole spectral function, measured momentum-resolved in angle-resolved photoemission spectroscopy (ARPES) or locally in scanning tunneling microscopy (STM), can be used to identify spin liquid materials. In this study, we employ tensor network methods to simulate the time evolution of a single hole doped into the Kitaev spin-liquid ground state. Focusing on the gapped spin liquid phase, we reveal two fundamentally different scenarios. For ferromagnetic spin couplings, the spin liquid is highly susceptible to hole doping: a Nagaoka ferromagnet forms dynamically around the doped hole, even at weak coupling. By contrast, in the case of antiferromagnetic spin couplings, the hole spectrum demonstrates an intricate interplay between charge, spin, and flux degrees of freedom, best described by a parton mean-field ansatz of fractionalized holons and spinons. Moreover, we find a good agreement of our numerical results to the analytically solvable case of slow holes. Our results demonstrate that dynamical hole spectral functions provide rich information on the structure of fractionalized quantum spin liquids.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}