Generalized Elitzur's Theorem and Dimensional Reduction

TL;DR

This paper generalizes Elitzur's theorem to systems with intermediate symmetries, formalizing the concept of dimensional reduction and applying it to various modern condensed matter systems.

Contribution

It introduces a generalized version of Elitzur's theorem applicable to systems with intermediate symmetries, expanding the theoretical framework.

Findings

Demonstrates dimensional reduction in diverse quantum systems

Provides theoretical foundation for understanding symmetry breaking

Applies to liquid crystals, orbital systems, and frustrated lattices

Abstract

We extend Elitzur's theorem to systems with symmetries intermediate between global and local. In general, our theorem formalizes the idea of {\it dimensional reduction}. We apply the results of this generalization to many systems that are of current interest. These include liquid crystalline phases of Quantum Hall systems, orbital systems, geometrically frustrated spin lattices, Bose metals, and models of superconducting arrays.