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Physical review. B, Condensed matter

Self-consistent mean-field approach for the ideal anyon gas

Lizeng Zhang, Michael Ma, Fu‐Chun Zhang

Published Nov 1, 1990• 14 citations
Publisher

Abstract

Using a self-consistent mean-field theory, where the anyon gauge field is approximated by its expectation value, we obtain a linear excitation spectrum for noninteracting anyon systems. The sound velocity is found to be \ensuremath{\surd}3 /2 of the value obtained by the random-phase approximation. The uniform liquid state of the anyon gas is shown to be locally stable against solid formation.

DOI
10.1103/physrevb.42.7894

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Using a self-consistent mean-field theory, where the anyon gauge field is approximated by its expectation value, we obtain a linear excitation spectrum for noninteracting anyon systems. The sound velocity is found to be \ensuremath{\surd}3 /2 of the value obtained by the random-phase approximation. The uniform liquid state of the anyon gas is shown to be locally stable against solid formation.
With the use of a self-consistent mean-field theory, where the anyon gauge field is approximated by its expectation value and the Coulomb interaction is calculated in the Hartree approximation, we have calculated the coupled acoustic anyon plasmon modes for an alternating-layered interacting anyon gas structure. In a single-layer system, we obtain a phonon mode for a noninteracting anyon gas. This is different from the result given by the random- phase approximation. When the Coulomb interaction is included, this phonon mode is suppressed. In a multi-layered system, we get an acoustic anyon plasmon mode with its sound velocity renormalized by the Coulomb interaction. The uniform liquid ground state is shown to be stable against solid crystallization.
We study a tight-binding model for anyons on a square lattice using a self-consistent mean-field theory, where the anyon gauge field is approximated by its expectation value. For any anyon density per site ${\mathrm{\ensuremath{\rho}}}_{0}$=p/q and statistics \ensuremath{\nu}=1-1/n, the anyon system has a linear collective mode if and only if q is greater than twice the largest common factor of p and n. The collective mode dispersion, \ensuremath{\omega}(k), is calculated numerically for n=1 (hard-core bosons) and n=2 (semions) at certain densities.
It is shown that the uniform ground state of ideal anyon gas can be constructed in the large-N collective field formalism and the excitation spectrum is given. It indicates that the system has a massless mode. In this treatment we employ a new set of gauge invariant variables to bypass the singularity which inevitably exists in the conventional density-phase variables. We also discuss the system of anyons including the delta function potential. The collective solution corresponding to Jackiw and Pi soliton is constructed.
We examine an approach to justifying the mean field approximation for the anyon gas, using the scattering of anyons. Parity violation permits a nonzero average scattering angle, from which one can extract a mean radius of curvature for anyons. If this is larger than the interparticle separation, one expects that the graininess of the statistical magnetic field is unimportant, and that the mean field approximation is good. We argue that a non-conventional interaction between anyons is crucial, in which case the criterion for validity of the approximation is identical to the one deduced using a self-consistency argument.
The ground and the excited states of a two-dimensional anyon system are studied via finite-size numerical calculations and single-mode approximation in a spherical geometry. It is shown that Laughlin's mean field theory gives an accurate description of the ground state properties. We find, consistent with earlier analytic theories, that the collective mode of the system exhibits a linear dispersion in the long wavelength limit, and predict a novel roton minimum at a finite value of the wavenumber q. We also discuss the consequences on the anyon spectrum of having a model repulsive interaction between the particles.