Gauge theory and mixed state criticality

TL;DR

This paper explores symmetry breaking and topological phases in mixed quantum states, using lattice gauge theory models to identify new phases and criticalities, including gapless symmetry-protected topological order.

Contribution

It introduces a framework for constructing and analyzing spontaneous symmetry breaking phases for strong symmetries in mixed states derived from lattice gauge theories.

Findings

New mixed-state topological phases identified

Models of criticality with gapless symmetry-protected topological order

Ground states of lattice gauge theories are purified states of mixed SSB states

Abstract

In mixed quantum states, the notion of symmetry is divided into two types: strong and weak symmetry. While spontaneous symmetry breaking (SSB) for a weak symmetry is detected by two-point correlation functions, SSB for a strong symmetry is characterized by the Renyi-2 correlators. In this work, we present a way to construct various SSB phases for strong symmetries, starting from the ground state phase diagram of lattice gauge theory models. In addition to introducing a new type of mixed-state topological phases, we provide models of the criticalities between them, including those with gapless symmetry-protected topological order. We clarify that the ground states of lattice gauge theories are purified states of the corresponding mixed SSB states. Our construction can be applied to any finite gauge theory and offers a framework to study quantum operations between mixed quantum phases.