A Bulk Spectral Gap in the Presence of Edge States for a Truncated Pseudopotential

Simone Warzel, Amanda Young

Research output: Contribution to journalArticlepeer-review

Abstract

We study the low-energy properties of a truncated Haldane pseudopotential with maximal half filling, which describes a strongly correlated system of spinless bosons in a cylinder geometry. For this Hamiltonian with either open or periodic boundary conditions, we prove a spectral gap above the highly degenerate ground-state space which is uniform in the volume and particle number. Our proofs rely on identifying invariant subspaces to which we apply gap-estimate methods previously developed only for quantum spin Hamiltonians. In the case of open boundary conditions, the lower bound on the spectral gap accurately reflects the presence of edge states, which do not persist into the bulk. Customizing the gap technique to the invariant subspace, we avoid the edge states and establish a more precise estimate on the bulk gap in the case of periodic boundary conditions.

Original languageEnglish (US)
Pages (from-to)133-178
Number of pages46
JournalAnnales Henri Poincare
Volume24
Issue number1
DOIs
StatePublished - Jan 2023
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

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