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

TL;DR

This paper proves a uniform spectral gap for a truncated Haldane pseudopotential system, revealing the influence of edge states in open boundary conditions and establishing a precise bulk gap estimate for periodic boundaries.

Contribution

It introduces a novel approach to estimate spectral gaps in strongly correlated bosonic systems with boundary effects, extending methods from quantum spin Hamiltonians.

Findings

Spectral gap exists above degenerate ground states in the model.

Edge states affect the spectral gap in open boundary conditions.

A more precise bulk gap estimate is achieved for periodic boundaries.

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.