Domain wall type defects as anyons in phase space

TL;DR

This paper presents a novel one-dimensional phase space formalism to understand the braiding properties of Laughlin quasi-particles in quantum Hall states, potentially extending to non-abelian states.

Contribution

It introduces a new phase space approach that simplifies the understanding of anyonic braiding in quantum Hall systems, with potential for generalization.

Findings

Formalism links 2D Hall liquid to 1D phase space

Laughlin quasi-holes as lattice soliton coherent states

Potential extension to non-abelian quantum Hall states

Abstract

We discuss how the braiding properties of Laughlin quasi-particles in quantum Hall states can be understood within a one-dimensional formalism we proposed earlier. In this formalism the two-dimensional space of the Hall liquid is identified with the phase space of a one-dimensional lattice system, and localized Laughlin quasi-holes can be understood as coherent states of lattice solitons. The formalism makes comparatively little use of the detailed structure of Laughlin wavefunctions, and may offer ways to be generalized to non-abelian states.