Crystalline equivalent boundary-bulk correspondence of two-dimensional topological phases

2021/12/29 by Jian-Hao Zhang, Zhang, Jian-Hao, Shang-Qiang Ning +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Physics of Superconductivity and Magnetism #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el) #Topological Materials and Phenomena

paper · pdf · doi:10.48550/arxiv.2112.14567

openalex publication_date 2021/12/29 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

The boundary of topological phases of matter can manifest its topology nature, which leads to the so-called boundary-bulk correspondence (BBC) of topological phases. In this Letter, we construct a one-to-one correspondence between the boundary theories of fermionic SPT (fSPT) phases protected by crystalline symmetry and on-site symmetry in 2D fermionic systems, which follow the so-called crystalline equivalence principle. We dub such correspondence crystalline equivalent BBC. We illustrate this correspondence by two simple examples and as an application, we discover the topological boundary theory of 2D fSPT phase with spin-1/2 fermions, protected by a non-Abelian group ℤ₄\rtimesℤ₂^T with A⁴=T²=P_f where A is the generator of ℤ₄, from its crystalline equivalent partner -- 2D higher-order fSPT phase with spinless fermions, protected by D₄ symmetry.

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