Approximate ground state of a confined Coulomb anyon gas in an external magnetic field

TL;DR

This paper presents an approximate analytic expression for the ground state energy of a confined Coulomb anyon gas in a magnetic field, validated against existing exact and numerical results.

Contribution

It introduces a variational approach with a regularization method to derive an approximate ground state energy formula for anyons in a magnetic field.

Findings

The derived expression matches well with known results in various regimes.

The method provides a practical way to estimate ground state energies for complex anyon systems.

Validation shows the approximation's accuracy across different parameters.

Abstract

We derive an analytic, albeit approximate, expression for the ground state energy of N Coulomb interacting anyons with fractional statistics nu, 0<= |nu| <= 1, confined in a two-dimensional well (with characteristic frequency omega_0 ) and subjected to an external magnetic field (with cyclotron frequency omega_c ). We apply a variational principle combined with a regularization procedure which consists of fitting a cut-off parameter to existing exact analytical results in the non-interacting case, and to numerical calculations for electrons in quantum dots in the interacting case. The resulting expression depends upon parameters of the system |nu|, N, omega_0, r_0, a_B and omega_c, where r_0 represents a characteristic unit length and a_B the Bohr radius. Validity of the result is critically assessed by comparison with exact, approximate, and numerical results from the literature.