Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals

TL;DR

This study uses diffusion quantum Monte Carlo to analyze three-dimensional Wigner crystals, identifying a phase transition at r_s=106 and comparing results with Hartree-Fock and Hartree theories to understand exchange and correlation effects.

Contribution

First diffusion quantum Monte Carlo calculations of 3D Wigner crystals across a range of densities, with optimized wave functions and analysis of phase transition and correlation effects.

Findings

Transition from ferromagnetic fluid to Wigner crystal at r_s=106

No improvement in wave functions using non-Gaussian orbitals

Comparison highlights role of exchange and correlation in Wigner crystals

Abstract

We report diffusion quantum Monte Carlo calculations of three-dimensional Wigner crystals in the density range r_s=100-150. We have tested different types of orbital for use in the approximate wave functions but none improve upon the simple Gaussian form. The Gaussian exponents are optimized by directly minimizing the diffusion quantum Monte Carlo energy. We have carefully investigated and sought to minimize the potential biases in our Monte Carlo results. We conclude that the uniform electron gas undergoes a transition from a ferromagnetic fluid to a body-centered-cubic Wigner crystal at r_s=106+/-1. The diffusion quantum Monte Carlo results are compared with those from Hartree-Fock and Hartree theory in order to understand the role played by exchange and correlation in Wigner crystals. We also study "floating" Wigner crystals and give results for their pair-correlation functions.