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. @article{xu_entanglement_2025,
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 = {2025-01-01},
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.},
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. |
Tang, N.; Gen, M.; Rotter, M.; Man, H.; Matsuhira, K.; Matsuo, A.; Kindo, K.; Ikeda, A.; Matsuda, Y.; Gegenwart, P.; Nakatsuji, S.; Kohama, Y. Crystal field magnetostriction of spin ice under ultrahigh magnetic fields Journal Article Phys. Rev. B 110, 214414, 2024. @article{tang_crystal_2024,
title = {Crystal field magnetostriction of spin ice under ultrahigh magnetic fields},
author = {N. Tang and M. Gen and M. Rotter and H. Man and K. Matsuhira and A. Matsuo and K. Kindo and A. Ikeda and Y. Matsuda and P. Gegenwart and S. Nakatsuji and Y. Kohama},
url = {https://link.aps.org/doi/10.1103/PhysRevB.110.214414},
doi = {10.1103/PhysRevB.110.214414},
year = {2024},
date = {2024-12-09},
urldate = {2024-12-01},
journal = {Phys. Rev. B},
volume = {110},
number = {21},
pages = {214414},
abstract = {We present a comprehensive study of the magnetoelastic properties of the Ising pyrochlore oxide Ho2Ti2O7, known as spin ice, by means of high-field magnetostriction measurements and numerical calculations. When a magnetic field is applied along the crystallographic ⟨111⟩ axis, the longitudinal magnetostriction exhibits a broad maximum in the low-field regime around 30 T, followed by a dramatic lattice contraction due to crystal-field (CF) level crossing at 𝐵cf∼65 T. The transverse magnetostriction exhibits a contrasting behavior, highlighting the anisotropic nature of the CF striction. By applying a magnetic field at varying sweep rates, we identify distinct timescales of spin dynamics that are relevant to monopole formation and annihilation, as well as CF-phonon dynamics. Our mean-field calculations, based on a point-charge model, successfully reproduce the overall magnetostriction behavior, revealing the competition between the exchange striction and CF striction. A signature of the CF level crossing is also observed through adiabatic magnetocaloric-effect measurements, consistent with our magnetostriction data.},
keywords = {B3, B5},
pubstate = {published},
tppubtype = {article}
}
We present a comprehensive study of the magnetoelastic properties of the Ising pyrochlore oxide Ho2Ti2O7, known as spin ice, by means of high-field magnetostriction measurements and numerical calculations. When a magnetic field is applied along the crystallographic ⟨111⟩ axis, the longitudinal magnetostriction exhibits a broad maximum in the low-field regime around 30 T, followed by a dramatic lattice contraction due to crystal-field (CF) level crossing at 𝐵cf∼65 T. The transverse magnetostriction exhibits a contrasting behavior, highlighting the anisotropic nature of the CF striction. By applying a magnetic field at varying sweep rates, we identify distinct timescales of spin dynamics that are relevant to monopole formation and annihilation, as well as CF-phonon dynamics. Our mean-field calculations, based on a point-charge model, successfully reproduce the overall magnetostriction behavior, revealing the competition between the exchange striction and CF striction. A signature of the CF level crossing is also observed through adiabatic magnetocaloric-effect measurements, consistent with our magnetostriction data. |
Abdeldaim, A. H.; Gretarsson, H.; Day, S. J.; Le, M. D.; Stenning, G. B. G.; Manuel, P.; Perry, R. S.; Tsirlin, A. A.; Nilsen, G. J.; Clark, L. Kitaev Interactions Through an Extended Superexchange Pathway in the jeff = 1/2 Ru3+ Honeycomb Magnet RuP3SiO11 Journal Article Nat. Commun. 15, 9778, 2024. @article{abdeldaim_kitaev_2024,
title = {Kitaev Interactions Through an Extended Superexchange Pathway in the j_{eff} = 1/2 Ru^{3+} Honeycomb Magnet RuP_{3}SiO_{11}},
author = {A. H. Abdeldaim and H. Gretarsson and S. J. Day and M. D. Le and G. B. G. Stenning and P. Manuel and R. S. Perry and A. A. Tsirlin and G. J. Nilsen and L. Clark},
doi = {10.1038/s41467-024-53900-3},
year = {2024},
date = {2024-11-15},
urldate = {2024-11-15},
journal = {Nat. Commun.},
volume = {15},
number = {1},
pages = {9778},
abstract = {Magnetic materials are composed of the simple building blocks of magnetic moments on a crystal lattice that interact via magnetic exchange. Yet from this simplicity emerges a remarkable diversity of magnetic states. Some reveal the deep quantum mechanical origins of magnetism, for example, quantum spin liquid (QSL) states in which magnetic moments remain disordered at low temperatures despite being strongly correlated through quantum entanglement. A promising theoretical model of a QSL is the Kitaev model, composed of unusual bond-dependent exchange interactions, but experimentally, this model is challenging to realise. Here we show that the material requirements for the Kitaev QSL survive an extended pseudo-edge-sharing superexchange pathway of Ru3+ octahedra within the honeycomb layers of the inorganic framework solid, RuP3SiO11. We confirm the requisite
state of Ru3+ in RuP3SiO11 and resolve the hierarchy of exchange interactions that provide experimental access to an unexplored region of the Kitaev model.},
keywords = {B1},
pubstate = {published},
tppubtype = {article}
}
Magnetic materials are composed of the simple building blocks of magnetic moments on a crystal lattice that interact via magnetic exchange. Yet from this simplicity emerges a remarkable diversity of magnetic states. Some reveal the deep quantum mechanical origins of magnetism, for example, quantum spin liquid (QSL) states in which magnetic moments remain disordered at low temperatures despite being strongly correlated through quantum entanglement. A promising theoretical model of a QSL is the Kitaev model, composed of unusual bond-dependent exchange interactions, but experimentally, this model is challenging to realise. Here we show that the material requirements for the Kitaev QSL survive an extended pseudo-edge-sharing superexchange pathway of Ru3+ octahedra within the honeycomb layers of the inorganic framework solid, RuP3SiO11. We confirm the requisite
state of Ru3+ in RuP3SiO11 and resolve the hierarchy of exchange interactions that provide experimental access to an unexplored region of the Kitaev model. |
