Spontaneous breaking of multipole symmetries

TL;DR

This paper investigates the conditions under which multipole symmetries, relevant to fracton physics and quantum dynamics, can be spontaneously broken, providing generalized theoretical arguments and explicit examples for their robustness or breaking.

Contribution

It develops generalized Mermin-Wagner and Imry-Ma arguments for the spontaneous breaking of multipole symmetries, advancing understanding of fracton phases and quantum dynamics.

Findings

Generalized Mermin-Wagner arguments for multipole symmetry breaking

Generalized Imry-Ma arguments for robustness against disorder

Explicit examples illustrating symmetry breaking and robustness

Abstract

Multipole symmetries are of interest both as a window on fracton physics and as a crucial ingredient in realizing new universality classes for quantum dynamics. Here we address the question of whether and when multipole symmetries can be spontaneously broken, both in thermal equilibrium and at zero temperature. We derive generalized Mermin-Wagner arguments for the total or partial breaking of multipolar symmetry groups and generalized Imry-Ma arguments for the robustness of such multipolar symmetry breaking to disorder. We present both general results and explicit examples. Our results should be directly applicable to quantum dynamics with multipolar symmetries and also provide a useful stepping stone to understanding the robustness of fracton phases to thermal fluctuations, quantum fluctuations, and disorder.