Symmetry-Enforced Topological Structures in Quantum Phase Diagrams
Abstract
We study the topological structure of the quantum phase diagram of gapped systems by identifying the noncontractibility of loops, so-called S1-families, within the gapped phase diagram in which many-body Hamiltonians can have nontrivial ground-state degeneracy. We manifest the role of symmetries in such S1-family classifications by the exotic symmetry interplay: (i) nontrivial mixed anomalies, (ii) semi-direct product relation between the spontaneously broken and the unbroken symmetries, and (iii) symmetry with noninvertible operators. We find that such structures lead to the novel S1-family classifications inaccessible by earlier classifications based on ``independent'' symmetries. Furthermore, we construct lattice realizations of these S1-families and explicitly demonstrate their novel algebraic structures.
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BibTeX
@misc{li2026symmetryenforced,
title = {{Symmetry-Enforced Topological Structures in Quantum Phase Diagrams}},
author = {Linhao Li and Yuan Yao},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29915},
eprint = {2608.29915},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29915},
}
RIS
TY - UNPB
TI - Symmetry-Enforced Topological Structures in Quantum Phase Diagrams
AU - Linhao Li
AU - Yuan Yao
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29915
UR - https://arxiv.org/abs/2608.29915
AB - We study the topological structure of the quantum phase diagram of gapped systems by identifying the noncontractibility of loops, so-called S^1-families, within the gapped phase diagram in which many-body Hamiltonians can have nontrivial ground-state degeneracy. We manifest the role of symmetries in such S^1-family classifications by the exotic symmetry interplay: (i) nontrivial mixed anomalies, (ii) semi-direct product relation between the spontaneously broken and the unbroken symmetries, and (iii) symmetry with noninvertible operators. We find that such structures lead to the novel S^1-family classifications inaccessible by earlier classifications based on ``independent'' symmetries. Furthermore, we construct lattice realizations of these S^1-families and explicitly demonstrate their novel algebraic structures.
ER -