Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance

TL;DR

This paper introduces a quasi-adiabatic continuation method for quantum states, demonstrating the robustness of topological ground state degeneracy and emergent gauge invariance in gapped or near-gapped quantum many-body systems.

Contribution

It develops a new technique for analyzing quantum states that preserves local properties and applies it to gauge theories and bosonic models, highlighting topological invariance.

Findings

Local gauge invariance is topological and robust against local perturbations.

Ground state degeneracy in emergent discrete gauge theories is stable.

The robustness of gauge invariance protects gapless gauge bosons.

Abstract

We define for quantum many-body systems a quasi-adiabatic continuation of quantum states. The continuation is valid when the Hamiltonian has a gap, or else has a sufficiently small low-energy density of states, and thus is away from a quantum phase transition. This continuation takes local operators into local operators, while approximately preserving the ground state expectation values. We apply this continuation to the problem of gauge theories coupled to matter, and propose a new distinction, perimeter law versus "zero law" to identify confinement. We also apply the continuation to local bosonic models with emergent gauge theories. We show that local gauge invariance is topological and cannot be broken by any local perturbations in the bosonic models in either continuous or discrete gauge groups. We show that the ground state degeneracy in emergent discrete gauge theories is a robust property of the bosonic model, and we argue that the robustness of local gauge invariance in the continuous case protects the gapless gauge boson.