Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems

Bruno Nachtergaele, Robert Sims, Amanda Young

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that uniformly small short-range perturbations do not close the bulk gap above the ground state of frustration-free quantum spin systems that satisfy a standard local topological quantum order condition. In contrast with earlier results, we do not require a positive lower bound for finite-system spectral gaps uniform in the system size. To obtain this result, we extend the Bravyi–Hastings–Michalakis strategy so it can be applied to perturbations of the GNS Hamiltonian of the infinite-system ground state.

Original languageEnglish (US)
JournalLetters in Mathematical Physics
Volume114
Issue number1
DOIs
StatePublished - Feb 2024

Keywords

  • 46L60
  • 81Q15
  • 82B10
  • 82B20
  • Bulk gap
  • Gapped ground state
  • GNS representation
  • Spectral gap stability
  • Topological insulator

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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