Symmetry-protected entangling boundary zero modes in crystalline topological insulators

Po Yao Chang, Christopher Mudry, Shinsei Ryu

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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.

Original languageEnglish (US)
Article numberP09014
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number9
StatePublished - Sep 1 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • correlation functions
  • correlation functions (theory)
  • entanglement in extended quantum systems (theory)
  • solvable lattice models


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