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

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.

arXiv comment8 pages, 3 figures

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Cited by in corpus (4)

• Wigner localization in two and three dimensions: an \emph{ab initio} approach
• A unique one-body position operator for periodic systems
• The localization spread and polarizability of rings and periodic chains
• The Wigner localization of interacting electrons in a one-dimensional harmonic potential