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.
- Score: 0.0
- 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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