Variational Excitations in Real Solids: Optical Gaps and Insights into Many-Body Perturbation Theory

TL;DR

This paper introduces a quantum Monte Carlo approach for accurately predicting optical gaps in solids, providing insights into the limitations of current density functionals and many-body perturbation theory.

Contribution

The authors develop a variational quantum Monte Carlo method for excited states in solids, achieving high accuracy and offering new insights into functional shortcomings.

Findings

Optical gaps predicted with 3.5% mean-absolute-deviation from experiment.

Method is insensitive to the choice of density functional.

Identifies a basis where perturbation theory's assumptions hold for ZnO.

Abstract

We present an approach to studying optical band gaps in real solids in which quantum Monte Carlo methods allow for the application of a rigorous variational principle to both ground and excited state wave functions. In tests that include small, medium, and large band gap materials, optical gaps are predicted with a mean-absolute-deviation of 3.5% against experiment, less than half the equivalent errors for typical many-body perturbation theories. The approach is designed to be insensitive to the choice of density functional, a property we exploit in order to provide insight into how far different functionals are from satisfying the assumptions of many body perturbation theory. We explore this question most deeply in the challenging case of ZnO, where we show that although many commonly used functionals have shortcomings, there does exist a one particle basis in which perturbation theory's zeroth order picture is sound. Insights of this nature should be useful in guiding the future application and improvement of these widely used techniques.