Classifying symmetric and symmetry-broken spin chain phases with anomalous group actions

• URL: http://arxiv.org/abs/2403.18573v1
• Date: Wed, 27 Mar 2024 13:54:45 GMT
• Title: Classifying symmetric and symmetry-broken spin chain phases with anomalous group actions
• Authors: Jose Garre Rubio, Andras Molnar, Yoshiko Ogata,
• Abstract summary: We consider the classification problem of quantum spin chains invariant under local decomposable group actions. We derive invariants for our classification that naturally cover one-dimensional symmetry protected topological phases.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 to 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 [J. Garre Rubio et al, Quantum 7, 927 (2023)] using matrix product states (MPSs) 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.

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