Ground states in relatively bounded quantum perturbations of classical lattice systems

TL;DR

This paper studies how classical lattice models' ground states are affected by quantum perturbations, proving stability and decay properties, and showing the AKLT model fits within this framework at large scales.

Contribution

It establishes general results on the stability and properties of ground states under relatively bounded quantum perturbations, including the AKLT model.

Findings

Existence of spectral gap under perturbations

Exponential decay of correlations

Analyticity of the ground state

Abstract

We consider ground states in relatively bounded quantum perturbations of classical lattice models. We prove general results about such perturbations (existence of the spectral gap, exponential decay of truncated correlations, analyticity of the ground state), and also prove that in particular the AKLT model belongs to this class if viewed at large enough scale. This immediately implies a general perturbation theory about this model.