Analytic approach to the ground-state energy of charged anyon gases

TL;DR

This paper presents an analytic formula for the ground-state energy of charged anyon gases, incorporating fractional statistics and Coulomb interactions, validated against various computational methods across different density regimes.

Contribution

The authors develop a novel analytic approach that models the ground-state energy of charged anyon gases by fitting to classical and quantum reference systems, bridging bosonic and fermionic behaviors.

Findings

Results closely match Monte Carlo calculations for bosons.

The formula indicates a nonmonotonous energy behavior for r_s ≤ 1.

The approach highlights the limitations of the Hartree-Fock approximation at certain densities.

Abstract

We derive an approximate analytic formula for the ground-state energy of the charged anyon gas. Our approach is based on the harmonically confined two-dimensional (2D) Coulomb anyon gas and a regularization procedure for vanishing confinement. To take into account the fractional statistics and Coulomb interaction we introduce a function, which depends on both the statistics and density parameters (nu and r_s, respectively). We determine this function by fitting to the ground state energies of the classical electron crystal at very large r_s (the 2D Wigner crystal), and to the Hartree-Fock (HF) energy of the spin-polarized 2D electron gas, and the dense 2D Coulomb Bose gas at very small r_s. The latter is calculated by use of the Bogoliubov approximation. Applied to the boson system (nu=0) our results are very close to recent results from Monte Carlo (MC) calculations. For spin-polarized electron systems (nu=1) our comparison leads to a critical judgment concerning the density range, to which the HF approximation and MC simulations apply. In dependence on nu, our analytic formula yields ground-state energies, which monotonously increase from the bosonic to the fermionic side if r_s > 1. For r_s leq 1 it shows a nonmonotonous behavior indicating a breakdown of the assumed continuous transformation of bosons into fermions by variation of the parameter nu .