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<p>We consider the classification problem of quantum spin chains invariant under local-decomposable group actions, covering matrix product unitaries (MPUs), using an operator algebraic approach. We focus on finite group symmetries hosting both symmetric and symmetry-broken phases. The local-decomposable group actions we consider have a 3-cocycle class of the symmetry group associated with them. We derive invariants for our classification that naturally cover one-dimensional symmetry-protected topological (SPT) phases. We prove that these invariants coincide with the ones of [<CitationRef CitationID="CR3">3</CitationRef>] using matrix product state (MPS) techniques, by explicitly working out the GNS representation of MPSs and MPUs, resulting in a useful dictionary between both approaches that could be of independent interest.</p>

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Classifying Symmetric and Symmetry-Broken Spin Chain Phases with Anomalous Group Actions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月16日

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  • José Garre Rubio,
  • Andras Molnar,
  • Yoshiko Ogata

摘要

We consider the classification problem of quantum spin chains invariant under local-decomposable group actions, covering matrix product unitaries (MPUs), using an operator algebraic approach. We focus on finite group symmetries hosting both symmetric and symmetry-broken phases. The local-decomposable group actions we consider have a 3-cocycle class of the symmetry group associated with them. We derive invariants for our classification that naturally cover one-dimensional symmetry-protected topological (SPT) phases. We prove that these invariants coincide with the ones of [3] using matrix product state (MPS) techniques, by explicitly working out the GNS representation of MPSs and MPUs, resulting in a useful dictionary between both approaches that could be of independent interest.