Non-Abelian Chern-Simons Particles in an External Magnetic Field
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.
Keywords
Cite
@article{arxiv.hep-th/9902028,
title = {Non-Abelian Chern-Simons Particles in an External Magnetic Field},
author = {Serguei B. Isakov and Gustavo Lozano and Stéphane Ouvry},
journal= {arXiv preprint arXiv:hep-th/9902028},
year = {2009}
}
Comments
35 pages, revtex, 3 eps figures included