Entanglement Asymmetry and Asymmetry Contour under Boundary Symmetry Breaking
Abstract
We investigate how symmetry-breaking boundary magnetic fields affect magnetization and Rényi-2 entanglement asymmetry (EA) in the transverse-field Ising model. For the ground state, magnetization exhibits qualitatively distinct behaviors in the ordered and disordered phases. EA also exhibits phase-dependent behavior, which is well captured by the lower and upper bounds derived in this work. In the critical regime, both magnetization and EA exhibit behavior qualitatively consistent with the field-theoretical predictions for a related setup. We also study boundary-quench dynamics and find that magnetization propagates from the boundary into the bulk with a velocity consistent with the maximum quasiparticle velocity. In contrast, because EA is a subsystem-integrated quantity, its spatial structure is not directly resolved. We therefore introduce the asymmetry contour, a contour-like finite-difference quantity that provides a spatially resolved characterization of the symmetry-breaking information encoded in the reduced density matrix. The resulting contour is complementary to the local magnetization, retaining sensitivity to nonlocal many-body correlations while its dynamics also reflects the underlying quasiparticle propagation. These results show how EA and its contour can provide complementary information-theoretic characterizations of symmetry breaking and its spatial structure.
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BibTeX
@misc{orito2026entanglement,
title = {{Entanglement Asymmetry and Asymmetry Contour under Boundary Symmetry Breaking}},
author = {Takahiro Orito and Daisuke Yamamoto},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32733},
eprint = {2610.32733},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32733},
}
RIS
TY - UNPB
TI - Entanglement Asymmetry and Asymmetry Contour under Boundary Symmetry Breaking
AU - Takahiro Orito
AU - Daisuke Yamamoto
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32733
UR - https://arxiv.org/abs/2610.32733
AB - We investigate how symmetry-breaking boundary magnetic fields affect magnetization and Rényi-2 entanglement asymmetry (EA) in the transverse-field Ising model. For the ground state, magnetization exhibits qualitatively distinct behaviors in the ordered and disordered phases. EA also exhibits phase-dependent behavior, which is well captured by the lower and upper bounds derived in this work. In the critical regime, both magnetization and EA exhibit behavior qualitatively consistent with the field-theoretical predictions for a related setup. We also study boundary-quench dynamics and find that magnetization propagates from the boundary into the bulk with a velocity consistent with the maximum quasiparticle velocity. In contrast, because EA is a subsystem-integrated quantity, its spatial structure is not directly resolved. We therefore introduce the asymmetry contour, a contour-like finite-difference quantity that provides a spatially resolved characterization of the symmetry-breaking information encoded in the reduced density matrix. The resulting contour is complementary to the local magnetization, retaining sensitivity to nonlocal many-body correlations while its dynamics also reflects the underlying quasiparticle propagation. These results show how EA and its contour can provide complementary information-theoretic characterizations of symmetry breaking and its spatial structure.
ER -