Automorphic equivalence within gapped phases of infinitely extended fermion systems

TL;DR

This paper proves automorphic equivalence in gapped phases of extended fermion and spin systems with decaying interactions, and applies it to establish a version of Goldstone's theorem for such systems.

Contribution

It introduces a proof of automorphic equivalence in gapped phases for systems with super-polynomial decay, extending understanding of symmetry invariance.

Findings

Automorphic equivalence holds in gapped phases with decaying interactions.

Gapped ground states are invariant under continuous symmetries.

A version of Goldstone's theorem is established for these systems.

Abstract

We prove automorphic equivalence within gapped phases of infinitely extended lattice fermion systems (as well as spin systems) with super-polynomially decaying interactions. As a simple application, we prove a version of Goldstone's theorem for such systems: if an infinite volume interaction is invariant under a continuous symmetry, then any gapped ground state is also invariant under that symmetry.