Classification of symmetry protected states of quantum spin chains for continuous symmetry groups

• URL: http://arxiv.org/abs/2409.01112v2
• Date: Mon, 7 Oct 2024 08:27:13 GMT
• Title: Classification of symmetry protected states of quantum spin chains for continuous symmetry groups
• Authors: Bruno de Oliveira Carvalho, Wojciech De Roeck, Tijl Jappens,
• Abstract summary: We show that SPT's corresponding to finite on-site symmetry groups $G$ are classified by the second cohomology group $H2(G,U(1))$. We also strengthen the existing results in the sense that our classification results hold within the class of spin chains with locally bounded on-site dimensions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Symmetry protected states (SPT's) of quantum spin systems were studied by several authors. For one-dimensional systems (spin chains), there is an essentially complete and rigorous understanding: SPT's corresponding to finite on-site symmetry groups $G$ are classified by the second cohomology group $H^2(G,U(1))$, as established by Kapustin et al. [J. Math. Phys. (2021)]. We extend this result to the case of compact topological symmetry groups $G$. We also strengthen the existing results in the sense that our classification results holds within the class of spin chains with locally bounded on-site dimensions.

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