Symmetry-Enforced Topological Structures in Quantum Phase Diagrams

Linhao Li; Yuan Yao

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arXiv · 2608.29915

Symmetry-Enforced Topological Structures in Quantum Phase Diagrams

Linhao Li·Yuan Yao

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Abstract

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.

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Linhao Li, Yuan Yao. 2026-08-30. Symmetry-Enforced Topological Structures in Quantum Phase Diagrams. https://arxiv.org/abs/2608.29915

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