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 $S^1$-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.

Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)

arXiv:2608.29915 [cond-mat.str-el]

(or arXiv:2608.29915v1 [cond-mat.str-el] for this version)

https://doi.org/10.48550/arXiv.2608.29915 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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