Ground-state energy of confined charged bosons in two dimensions

TL;DR

This study combines Pade approximant and variational Monte Carlo methods to accurately determine the ground-state energy of confined charged bosons in two dimensions, providing analytic expressions and validating results across densities.

Contribution

It introduces a combined approach using Pade approximants and Monte Carlo simulations to accurately estimate ground-state energies of 2D charged bosons in a trap, with validated low-error results.

Findings

Pade approximant error is less than 4% across densities

Analytic expressions for ground-state energy are derived

Method is accurate in dilute and high-density limits

Abstract

The Pade approximant technique and the variational Monte Carlo method are applied to determine the ground-state energy of a finite number of charged bosons in two dimensions confined by a parabolic trap. The particles interact repulsively through a Coulombic, 1/r, potential. Analytic expressions for the ground-state energy are obtained. The convergence of the Pade sequence and comparison with the Monte Carlo results show that the error of the Pade estimate is less than 4% at any boson density and is exact in the extreme situations of very dilute and high density.