Lattice Symmetry Remnants in Spatial and Temporal Entanglement of Quantum Critical Spin Chains
Abstract
Quantum critical lattice models retain universal information about their lattice symmetries beyond the bulk data of their infrared conformal field theory (CFT). We probe these lattice symmetry remnants by comparing the spatial and temporal entanglement of two Euclidean-evolved states from the same critical model. At large length scales, short-range initial states define conformal boundaries and boundary CFT (BCFT) organizes the universal low-lying entanglement spectrum. In the temporal construction, the translation invariance along Euclidean time requires a uniform state. Moreover, the time slice δτ→ 0 forces a split-gate basis, resulting in a new regular uniform symmetry-preserving transfer representation. For the Ising and Potts chains, onsite symmetries result in the same BCFT structure in the spatial and temporal constructions. The spin-1/2 XXZ chain instead realizes the Lieb--Schultz--Mattis (LSM) constraint differently in the two Euclidean quantization. A U(1)-preserving spatial state has a doubled unit cell and inequivalent entanglement cuts, whereas the temporal state remains uniform and alternates between translation relation related Dirichlet sectors with integer and half-integer compact-boson zero modes. Breaking U(1) removes the zero mode and the alternation. Thus microscopic symmetry and anomaly data remain visible in universal entanglement by constraining the boundary realization of the infrared CFT.
Related
- Critical Touching of Temporal Entanglement Transitions
- Predicting Entanglement Spectra of Gapless Symmetry-Protected Topological States in One Dimension
- Ground-state entanglement and preserved dynamical symmetry in the interacting boson model
- Temporal entanglement transition in chaotic quantum many-body dynamics
- Symmetry-resolved quasilocal entanglement as a key to Mott and pseudogap physics in plaquette CDMFT
BibTeX
@misc{yang2026lattice,
title = {{Lattice Symmetry Remnants in Spatial and Temporal Entanglement of Quantum Critical Spin Chains}},
author = {Xiao-Han Yang and Rui-Zhen Huang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31676},
eprint = {2610.31676},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31676},
}
RIS
TY - UNPB
TI - Lattice Symmetry Remnants in Spatial and Temporal Entanglement of Quantum Critical Spin Chains
AU - Xiao-Han Yang
AU - Rui-Zhen Huang
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.31676
UR - https://arxiv.org/abs/2610.31676
AB - Quantum critical lattice models retain universal information about their lattice symmetries beyond the bulk data of their infrared conformal field theory (CFT). We probe these lattice symmetry remnants by comparing the spatial and temporal entanglement of two Euclidean-evolved states from the same critical model. At large length scales, short-range initial states define conformal boundaries and boundary CFT (BCFT) organizes the universal low-lying entanglement spectrum. In the temporal construction, the translation invariance along Euclidean time requires a uniform state. Moreover, the time slice δτ→ 0 forces a split-gate basis, resulting in a new regular uniform symmetry-preserving transfer representation. For the Ising and Potts chains, onsite symmetries result in the same BCFT structure in the spatial and temporal constructions. The spin-1/2 XXZ chain instead realizes the Lieb--Schultz--Mattis (LSM) constraint differently in the two Euclidean quantization. A U(1)-preserving spatial state has a doubled unit cell and inequivalent entanglement cuts, whereas the temporal state remains uniform and alternates between translation relation related Dirichlet sectors with integer and half-integer compact-boson zero modes. Breaking U(1) removes the zero mode and the alternation. Thus microscopic symmetry and anomaly data remain visible in universal entanglement by constraining the boundary realization of the infrared CFT.
ER -