Work

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

Year: 2026

Type: article

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 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.

Source: Annales Henri Poincaré

DOI: 10.1007/s00023-026-01717-9

Authors: José Garre Rubio, Andras Molnar, Yoshiko Ogata

Institutions: University of Vienna, Kyoto University, Research Institute for Mathematical Sciences, Kyoto University

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090