Backflow Correlations for the Electron Gas and Metallic Hydrogen

TL;DR

This paper develops and evaluates backflow-threebody wavefunctions for electrons and protons, demonstrating their effectiveness in variational and diffusion Monte Carlo calculations for electron gas and metallic hydrogen, with improved energy estimates and flexibility.

Contribution

It introduces a new analytical form of backflow wavefunctions for electron-proton systems and demonstrates their advantages over traditional density functional methods.

Findings

Lower energies for electron gas than previous methods.

Nearly optimal energies for bcc hydrogen using backflow wavefunctions.

Fewer parameters needed compared to density functional solutions.

Abstract

We justify and evaluate backflow-threebody wavefunctions for a two component system of electrons and protons. Based on the generalized Feynman-Kacs formula, many-body perturbation theory, and band structure calculations, we analyze the use and the analytical form of the backflow function from different points of view. The resulting wavefunctions are used in Variational and Diffusion Monte Carlo calculations of the electron gas and of solid and liquid metallic hydrogen. For the electron gas, the purely analytic backflow and three-body form gives lower energies than those of previous calculations. For bcc hydrogen, analytical and optimized backflow-threebody wavefunctions lead to energies nearly as low as those from using LDA orbitals in the trial wavefunction. However, compared to wavefunctions constructed from density functional solutions, backflow wavefunctions have the advantage of only few parameters to estimate, the ability to include easily and accurately electron-electron correlations, and that they can be directly generalized from the crystal to a disordered liquid of protons.