Stability of Gapped Ground State Phases of Spins and Fermions in One Dimension

TL;DR

This paper proves explicit lower bounds on spectral gaps in one-dimensional quantum systems with open boundaries, showing their stability under weak perturbations assuming local topological order.

Contribution

It introduces a method to explicitly bound spectral gaps in 1D frustration-free quantum chains considering boundary effects and local topological order.

Findings

Spectral gaps are stable under weak perturbations.

Explicit lower bounds on ground state gaps are derived.

Analysis includes bulk and edge effects on spectral gaps.

Abstract

We investigate the persistence of spectral gaps of one-dimensional frustration free quantum lattice systems under weak perturbations and with open boundary conditions. Assuming the interactions of the system satisfy a form of local topological quantum order, we prove explicit lower bounds on the ground state spectral gap and higher gaps for spin and fermion chains. By adapting previous methods using the spectral flow, we analyze the bulk and edge dependence of lower bounds on spectral gaps.