Fractionalization of itinerant anyons in one dimensional chains

TL;DR

This paper models interacting itinerant non-Abelian anyons in one-dimensional chains, revealing a fractionalization into charge and anyonic degrees of freedom akin to spin-charge separation in Luttinger liquids.

Contribution

It introduces effective anyonic t-J models for itinerant non-Abelian anyons and demonstrates fractionalization phenomena through exact diagonalization.

Findings

Fractionalization of anyons into charge and non-Abelian sectors

Coupling between charge and anyonic excitations at microscopic level

Spectral analysis combining charge and anyonic sectors

Abstract

We construct models of interacting itinerant non-Abelian anyons moving along one-dimensional chains, focusing in particular on itinerant Ising anyon chains, and derive effective anyonic t-J models for the low energy sectors. Solving these models by exact diagonalization, we find a fractionalization of the anyons into charge and (non-Abelian) anyonic degrees of freedom -- a generalization of spin-charge separation of electrons which occurs in Luttinger liquids. A detailed description of the excitation spectrum by combining spectra for charge and anyonic sectors requires a subtle coupling between charge and anyonic excitations at the microscopic level (which we also find to be present in Luttinger liquids), despite the macroscopic fractionalization.