Ab initio electronic density in solids by many-body plane-wave auxiliary-field quantum Monte Carlo calculations

TL;DR

This paper demonstrates the use of ab initio auxiliary-field quantum Monte Carlo in a plane-wave basis to accurately compute electronic densities in solids, enabling advanced analysis of correlation functions and thermodynamic properties.

Contribution

It introduces a novel implementation of AFQMC for calculating electronic densities and correlation functions in solids within a plane-wave framework, including back-propagation techniques.

Findings

Accurate electronic densities for Si, NaCl, and Cu.

Analysis of finite supercell size effects on densities.

Benchmarking of density functionals against near-exact AFQMC results.

Abstract

We present accurate many-body results of the electronic densities in several solid materials, including Si, NaCl, and Cu. These results are obtained using the ab initio auxiliary-field quantum Monte Carlo (AFQMC) method working in a plane-wave basis with norm-conserving, multiple-projector pseudopotentials. AFQMC has been shown to be an excellent many-body total energy method. Computation of observables and correlation functions other than the ground-state energy requires back-propagation, whose adaption and implementation in the plane-wave basis AFQMC framework are discussed in the present paper. This development allows us to compute correlation functions, electronic densities and interatomic forces, paving the way for geometry optimizations and calculations of thermodynamic properties in solids. Finite supercell size effects are considerably more subtle in the many-body framework than in independent-electron calculations. We analyze the convergence of the electronic density, and obtain best estimates for the thermodynamic limit. The densities from several typical density functionals are benchmarked against our near-exact results. The electronic densities we have obtained can also be used to help construct improved density functionals.