From Lieb-Robinson Bounds to Automorphic Equivalence

TL;DR

This paper reviews how Lieb-Robinson bounds help understand locality in quantum lattice systems and demonstrates the equivalence of two definitions of gapped ground state phases.

Contribution

It clarifies the relationship between different definitions of gapped ground state phases using Lieb-Robinson bounds.

Findings

Lieb-Robinson bounds characterize locality in quantum dynamics.

Two definitions of gapped ground state phases are shown to be equivalent.

Abstract

I review the role of Lieb-Robinson bounds in characterizing and utilizing the locality properties of the Heisenberg dynamics of quantum lattice systems. In particular, I discuss two definitions of gapped ground state phases and show that they are essentially equivalent.