Symmetry-Enforced Topological Structures in Quantum Phase Diagrams

• URL: http://arxiv.org/abs/2608.29915v1
• Date: Sun, 30 Aug 2026 17:19:06 GMT
• Title: Symmetry-Enforced Topological Structures in Quantum Phase Diagrams
• Abstract summary: We study the noncontractibility of loops, so-called $S1$-families, within the gapped phase diagram in which many-body Hamiltonians can have nontrivial ground-state degeneracy.<n>We find that such structures lead to the novel $S1$-family classifications inaccessible by earlier classifications based on independent'' symmetries.
• Score: 7.727969651316747
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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