2014/03/31 by Po-Yao Chang, Christopher Mudry, Shinsei Ryu
Materials Science · Mathematics · Physics and Astronomy · #Boundary (topology) #Combinatorics #Condensed matter physics #Geometry #Graphene research and applications #Mathematical analysis #Mathematics #Physics #Quantum many-body systems #Quantum mechanics #Symmetry (geometry) #Symmetry protected topological order #Theoretical physics #Topological Materials and Phenomena #Topological insulator #Topological order #Topology (electrical circuits) #Zero (linguistics) #Zero-point energy #cond-mat.str-el
paper · pdf · doi:10.1088/1742-5468/2014/09/p09014
published as J. Stat. Mech. (2014) P09014 · 88 pages, 16 figures, Table of contents added, published version in JSTAT Special Issue: Quantum Entanglement in Condensed Matter Physics
openalex publication_date 2014/09/16 · arxiv created 2014/09/22 · arxiv updated 2014/11/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Crystalline topological insulators owe their topological character to the protection that certain boundary states acquire because of certain point-group symmetries. We first show that a Hermitian operator obeying supersymmetric quantum mechanisms (SUSY QM) delivers the entanglement spectrum. We then show that such an entanglement spectrum that is compatible with a certain point-group symmetry obeys a certain local spectral symmetry. The latter result is applied to the stability analysis of four fermionic non-interacting Hamiltonians, the last of which describes graphene with a Kekule distortion. All examples have the remarkable property that their entanglement spectra inherit a local spectral symmetry from either an inversion or reflection symmetry that guarantees the stability of gapless boundary entangling states, even though all examples fail to support protected gapless boundary states at their physical boundaries.