Mermin-Wagner theorems for quantum systems with multipole symmetries

TL;DR

This paper extends Mermin-Wagner theorems to quantum lattice systems with multipole symmetries, demonstrating that higher-order symmetries prevent the breaking of lower-order ones and increase the critical dimension for symmetry breaking.

Contribution

It proves Mermin-Wagner-type theorems for quantum systems with multipole symmetries, revealing how higher symmetries protect against lower symmetry breaking.

Findings

Higher multipole symmetries increase the critical dimension for charge symmetry breaking.

Charge symmetry cannot be broken in dimensions below the critical dimension with multipole symmetries.

The critical dimension for symmetry breaking is increased to d=4 with dipole symmetry on a0a0a0a0a0a0a0a0a0a0a0a0a0a0a0 lattice.

Abstract

We prove Mermin-Wagner-type theorems for quantum lattice systems in the presence of multipole symmetries. These theorems show that the presence of higher-order symmetries protects against the breaking of lower-order ones. In particular, we prove that the critical dimension in which the charge symmetry can be broken increases if the system admits higher multipole symmetries, e.g. $ d = 4 $ on the regular lattice $ \mathbb{Z}^d $ in the presence of dipole symmetry.