Analytic approach to the ground state energy of charged anyon gases in the high magnetic field

TL;DR

This paper derives analytic formulas for the ground state energy of 2D charged anyon gases in high magnetic fields, incorporating fractional statistics and Coulomb interactions, applicable across a range of anyon parameters.

Contribution

It introduces new analytic expressions for the ground state energy of charged anyon gases in strong magnetic fields, including Coulomb interactions, using harmonic potential regularization and fitting to known quantum Hall data.

Findings

Exact formula for non-interacting case.

Fitted function for Coulomb interaction case.

Applicable to anyons with 0 ≤ ν ≤ 1.

Abstract

We present analytic formulas for the ground state energy of the two-dimensional (2D) anyon gas in the quantum limit of a perpendicular magnetic field (Landau level filling factor \nu_L\le 1). These formulas, for the cases without and with Coulomb interaction, are obtained by applying the harmonic potential regularization for vanishing confinement to the harmonically confined Coulomb anyon gas as in our previous paper for the case without magnetic field. For the case without Coulomb interaction our analytic expression is exact. It contains a contribution deriving from the anyon gauge field (characterizing the fractional statistics by the anyon parameter \nu) and depends on \nu and \nu_L. For the case with Coulomb interaction we introduce a function, depending on \nu, \nu_L and the density parameter r_s, which is determined by fitting to the interpolation formula of Fano and Ortolani in the fractional quantum Hall regime for spin-polarized fermions in conjunction with results of Yoshioka for the ground state energy of the 2D Coulomb boson gas in high magnetic fields. With their dependence on \nu, our formulas apply not only to fermions (\nu=1) but quite generally to anyons (0\le \nu\le 1).