One-dimensional symmetric phases protected by frieze symmetries

• URL: http://arxiv.org/abs/2202.12880v2
• Date: Wed, 13 Jul 2022 13:52:47 GMT
• Title: One-dimensional symmetric phases protected by frieze symmetries
• Authors: Bram Vancraeynest-De Cuiper, Jacob C. Bridgeman, Nicolas Dewolf, Jutho Haegeman, Frank Verstraete
• Abstract summary: We make a systematic study of symmetry-protected topological gapped phases of quantum spin chains in the presence of the frieze space groups in one dimension using matrix product states. We identify seventeen distinct non-trivial phases, define canonical forms, and compare the topological indices obtained from the MPS analysis with the group cohomological predictions.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We make a systematic study of symmetry-protected topological gapped phases of quantum spin chains in the presence of the frieze space groups in one dimension using matrix product states. Here, the spatial symmetries of the one-dimensional lattice are considered together with an additional 'vertical reflection', which we take to be an on-site $\mathbb{Z}_2$ symmetry. We identify seventeen distinct non-trivial phases, define canonical forms, and compare the topological indices obtained from the MPS analysis with the group cohomological predictions. We furthermore construct explicit renormalization group fixed-point wave functions for symmetry-protected topological phases with global on-site symmetries, possibly combined with time-reversal and parity symmetry. En route, we demonstrate how group cohomology can be computed using the Smith normal form.

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