Non-Abelian Chern-Simons Particles in an External Magnetic Field

TL;DR

This paper investigates the quantum mechanics and thermodynamics of non-Abelian Chern-Simons particles in magnetic fields, revealing unique step-wise behavior in virial coefficients and relations to SU(2) bosons.

Contribution

It derives the N-body Hamiltonian for non-Abelian anyons in a magnetic field and analyzes their thermodynamic properties, highlighting differences from Abelian anyons.

Findings

Virial coefficient exhibits step-wise dependence on the statistics parameter in strong magnetic fields.

N-body spectrum depends linearly on the coupling when a harmonic potential is present.

Cluster coefficients cancel dependence on the statistics parameter for small values.

Abstract

The quantum mechanics and thermodynamics of SU(2) non-Abelian Chern-Simons particles (non-Abelian anyons) in an external magnetic field are addressed. We derive the N-body Hamiltonian in the (anti-)holomorphic gauge when the Hilbert space is projected onto the lowest Landau level of the magnetic field. In the presence of an additional harmonic potential, the N-body spectrum depends linearly on the coupling (statistics) parameter. We calculate the second virial coefficient and find that in the strong magnetic field limit it develops a step-wise behavior as a function of the statistics parameter, in contrast to the linear dependence in the case of Abelian anyons. For small enough values of the statistics parameter we relate the N-body partition functions in the lowest Landau level to those of SU(2) bosons and find that the cluster (and virial) coefficients dependence on the statistics parameter cancels.