Commensurate and Incommensurate States of Topological Quantum Matter

TL;DR

This paper demonstrates the existence of modulated, commensurate, and incommensurate states in topological quantum matter systems of parafermions, revealing a new Lifshitz universality class with a topological tricritical point.

Contribution

It introduces the Lifshitz topological universality class and characterizes its phase diagram, including a topological tricritical point, through numerical and duality methods.

Findings

Identification of a Lifshitz universality class in topological matter

Discovery of a topological tricritical point with three distinct phases

Numerical and duality evidence for modulated topological states

Abstract

We prove numerically and by dualities the existence of modulated, commensurate and incommensurate states of topological quantum matter in simple systems of parafermions, motivated by recent proposals for the realization of such systems in mesoscopic arrays. In two space dimensions, we obtain the simplest representative of a topological universality class that we call Lifshitz. It is characterized by a topological tricritical point where a non-locally ordered homogeneous phase meets a disordered phase and a third phase that displays modulations of a non-local order parameter.