Intermediate Symmetries In Electronic Systems: Dimensional Reduction, Order Out Of Disorder, Dualities, And Fractionalization

TL;DR

This paper explores intermediate symmetries in various electronic systems, revealing how they enable dimensional reduction, dualities, and unconventional orders such as topological and multiparticle orders, expanding understanding of complex quantum phases.

Contribution

It formalizes the concept of intermediate symmetries and applies it to diverse systems, uncovering dualities and novel order phenomena driven by these symmetries.

Findings

Identification of dualities between different systems via space-time reflection symmetries

Demonstration of 'order out of disorder' phenomena in certain systems

Discovery of multiparticle and topological orders enabled by dimensional reduction

Abstract

We discuss symmetries intermediate between global and local and formalize the notion of dimensional reduction adduced from such symmetries. We apply this generalization to several systems including liquid crystalline phases of Quantum Hall systems, transition metal orbital systems, frustrated spin systems, (p+ip) superconducting arrays, and sliding Luttinger liquids. By considering space-time reflection symmetries, we illustrate that several of these systems are dual to each other. In some systems exhibiting these symmetries, low temperature local orders emerge by an "order out of disorder" effect while in other systems, the dimensional reduction precludes standard orders yet allows for multiparticle orders (including those of a topological nature).