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Real-space recipes for general topological crystalline states

Author

Listed:
  • Zhida Song

    (Chinese Academy of Sciences
    University of Chinese Academy of Sciences
    Princeton University)

  • Chen Fang

    (Chinese Academy of Sciences
    Kavli Institute for Theoretical Sciences, Chinese Academy of Sciences
    CAS Center for Excellence in Topological Quantum Computation
    Songshan Lake Laboratory For Materials Science)

  • Yang Qi

    (Fudan University
    Fudan University
    Collaborative Innovation Center of Advanced Microstructures)

Abstract

Topological crystalline states (TCSs) are short-range entangled states jointly protected by onsite and crystalline symmetries. Here we present a unified scheme for constructing all TCSs, bosonic and fermionic, free and interacting, from real-space building blocks and connectors. Building blocks are lower-dimensional topological states protected by onsite symmetries alone, and connectors are glues that complete the open edges shared by two or multiple building blocks. The resulted assemblies are selected against two physical criteria we call the no-open-edge condition and the bubble equivalence. The scheme is then applied to obtaining the full classification of bosonic TCSs protected by several onsite symmetry groups and each of the 17 wallpaper groups in two dimensions and 230 space groups in three dimensions. We claim that our construction scheme can give the complete set of TCSs for bosons and fermions, and prove the boson case analytically using a spectral-sequence expansion.

Suggested Citation

  • Zhida Song & Chen Fang & Yang Qi, 2020. "Real-space recipes for general topological crystalline states," Nature Communications, Nature, vol. 11(1), pages 1-14, December.
    • Handle: RePEc:nat:natcom:v:11:y:2020:i:1:d:10.1038_s41467-020-17685-5
    DOI: 10.1038/s41467-020-17685-5
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