Monte Carlo simulations of two-dimensional charged bosons

TL;DR

This paper uses quantum Monte Carlo simulations to study the ground state properties of two-dimensional charged bosons, predicting Wigner crystallization at high coupling and analyzing various physical properties across the fluid phase.

Contribution

It provides comprehensive Monte Carlo calculations of ground state properties, including energy, momentum distribution, and excitation energies, with analytic formulas and phase transition predictions.

Findings

Wigner crystallization predicted at r_s ≈ 60

Condensate fraction is less than 1 near freezing

Derived bounds and formulas for excitation energies

Abstract

Quantum Monte Carlo methods are used to calculate various ground state properties of charged bosons in two dimensions, throughout the whole density range where the fluid phase is stable. Wigner crystallization is predicted at $r_s\simeq 60$. Results for the ground state energy and the momentum distribution are summarized in analytic interpolation formulas embodying known asymptotic behaviors. Near freezing, the condensate fraction is less than 1%. The static structure factor $S(k)$ and susceptibility $\chi(k)$ are obtained from the density-density correlation function in imaginary time, $F({\bf k},\tau)$. An estimate of the energy of elementary excitations, given in terms of an upper bound involving $S(k)$ and $\chi(k)$, is compared with the result obtained via analytic continuation from $F({\bf k},\tau)$.