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One-dimensional symmetric phases protected by frieze symmetries

(2023) PHYSICAL REVIEW B. 107(11).
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Abstract
We undertake a systematic study of symmetry-protected topological gapped phases of quantum spin chains in the presence of the quasi-one-dimensional frieze space groups. 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 Z2 symmetry. We identify seventeen distinct non-trivial phases and define canonical forms. If time-reversal is combined with a shift over one site, then no new topological phases arise. We furthermore construct explicit renormalization-group fixed point wavefunctions for symmetry-protected topological phases with global on-site symmetries, and demonstrate how group cohomology can be computed using the Smith normal form.
Keywords
symmetry, group theory, tensor network, physics, theoretical physics, MATRIX

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MLA
Vancraeynest-De Cuiper, Bram, et al. “One-Dimensional Symmetric Phases Protected by Frieze Symmetries.” PHYSICAL REVIEW B, vol. 107, no. 11, 2023, doi:10.1103/PhysRevB.107.115123.
APA
Vancraeynest-De Cuiper, B., Bridgeman, J. C., Dewolf, N., Haegeman, J., & Verstraete, F. (2023). One-dimensional symmetric phases protected by frieze symmetries. PHYSICAL REVIEW B, 107(11). https://doi.org/10.1103/PhysRevB.107.115123
Chicago author-date
Vancraeynest-De Cuiper, Bram, Jacob C Bridgeman, Nicolas Dewolf, Jutho Haegeman, and Frank Verstraete. 2023. “One-Dimensional Symmetric Phases Protected by Frieze Symmetries.” PHYSICAL REVIEW B 107 (11). https://doi.org/10.1103/PhysRevB.107.115123.
Chicago author-date (all authors)
Vancraeynest-De Cuiper, Bram, Jacob C Bridgeman, Nicolas Dewolf, Jutho Haegeman, and Frank Verstraete. 2023. “One-Dimensional Symmetric Phases Protected by Frieze Symmetries.” PHYSICAL REVIEW B 107 (11). doi:10.1103/PhysRevB.107.115123.
Vancouver
1.
Vancraeynest-De Cuiper B, Bridgeman JC, Dewolf N, Haegeman J, Verstraete F. One-dimensional symmetric phases protected by frieze symmetries. PHYSICAL REVIEW B. 2023;107(11).
IEEE
[1]
B. Vancraeynest-De Cuiper, J. C. Bridgeman, N. Dewolf, J. Haegeman, and F. Verstraete, “One-dimensional symmetric phases protected by frieze symmetries,” PHYSICAL REVIEW B, vol. 107, no. 11, 2023.
@article{8743031,
  abstract     = {{We undertake a systematic study of symmetry-protected topological gapped phases of quantum spin chains in the presence of the quasi-one-dimensional frieze space groups. 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 Z2 symmetry. We identify seventeen distinct non-trivial phases and define canonical forms. If time-reversal is combined with a shift over one site, then no new topological phases arise. We furthermore construct explicit renormalization-group fixed point wavefunctions for symmetry-protected topological phases with global on-site symmetries, and demonstrate how group cohomology can be computed using the Smith normal form.}},
  articleno    = {{115123}},
  author       = {{Vancraeynest-De Cuiper, Bram and Bridgeman, Jacob C and Dewolf, Nicolas and Haegeman, Jutho and Verstraete, Frank}},
  issn         = {{2469-9950}},
  journal      = {{PHYSICAL REVIEW B}},
  keywords     = {{symmetry,group theory,tensor network,physics,theoretical physics,MATRIX}},
  language     = {{eng}},
  number       = {{11}},
  pages        = {{14}},
  title        = {{One-dimensional symmetric phases protected by frieze symmetries}},
  url          = {{http://doi.org/10.1103/PhysRevB.107.115123}},
  volume       = {{107}},
  year         = {{2023}},
}

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