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.

35 pages, revtex, 3 eps figures included

References in corpus (3)

• Landau-Ginzburg Theories for Non-Abelian Quantum Hall States
• Exclusion Statistics in Conformal Field Theory Spectra
• Exclusion statistics for non-abelian quantum Hall states

Cited by in corpus (6)

• New spin Calogero-Sutherland models related to B_N-type Dunkl operators
• Exact solutions of an elliptic Calogero--Sutherland model
• Anyons and lowest Landau level Anyons
• Free harmonic oscillators, Jack polynomials and Calogero-Sutherland systems
• A Unified Algebraic Approach to Few and Many-Body Correlated Systems
• The Lowest Landau Level Anyon Equation of State in the Anti-screening Regime