Accurate ground-state energies of Wigner crystals from a simple real-space approach

TL;DR

This paper introduces a straightforward real-space method to accurately compute the ground-state energies of Wigner crystals in various dimensions, improving precision and revealing notable differences in harmonic corrections compared to previous studies.

Contribution

It presents a novel, simple real-space approach using Clifford boundary conditions and renormalized Coulomb potential for precise energy calculations of Wigner crystals.

Findings

Higher precision in energy calculations compared to literature

Significant difference in harmonic correction for 2D Wigner crystal

Classical energies of various lattice structures reported

Abstract

We propose a simple and efficient real-space approach for the calculation of the ground-state energies of Wigner crystals in 1, 2, and 3 dimensions. To be precise, we calculate the first two terms in the asymptotic expansion of the total energy per electron which correspond to the classical energy and the harmonic correction due to the zero-point motion of the Wigner crystals, respectively. Our approach employs Clifford periodic boundary conditions to simulate the infinite electron gas and a renormalized distance to evaluate the Coulomb potential. This allows us to calculate the energies unambiguously and with a higher precision than those reported in the literature. Our results are in agreement with the literature values with the exception of harmonic correction of the 2-dimensional Wigner crystal for which we find a significant difference. Although we focus on the ground state, i.e., the triangular lattice and the body-centered cubic lattice, in two and three dimensions, respectively, we also report the classical energies of several other common lattice structures.