One-Dimensional XXZ Model for Particles Obeying Fractional Statistics

TL;DR

This paper introduces a one-dimensional model for particles with fractional statistics, solving it exactly using the Bethe Ansatz, and revealing how fractional statistics emulate coupling to an external gauge field.

Contribution

It presents an exact solution for an $XXZ$ model with particles obeying fractional statistics, linking fractional statistics to gauge field coupling.

Findings

Exact solution of the $XXZ$ model with fractional statistics particles

Bethe equations demonstrate the effect of fractional statistics as gauge coupling

Fractional statistics effectively simulate external gauge field interactions

Abstract

We define one-dimensional particles as non-abelian representations of the symmetric group $S_N$. The exact solution of an $XXZ$ type Hamiltonian built up with such particles is achieved using the coordinate Bethe Ansatz. The Bethe equations show that fractional statistics, effectively, accounts for coupling an external gauge field to an integer statistics' system.