Auxiliary field quantum Monte Carlo at the basis set limit: application to lattice constants

TL;DR

This paper introduces a plane-wave implementation of auxiliary-field quantum Monte Carlo within the PAW formalism, achieving basis set limit accuracy for lattice constants and providing a benchmark for condensed matter properties.

Contribution

The authors develop an exact inversion approach for AFQMC in VASP, enabling basis set limit calculations and systematic correction of correlation effects in solids.

Findings

Achieves 0.14% mean absolute relative error in lattice constants

Demonstrates AFQMC corrects long-range screening deficiencies of MP2 and RPA

Identifies RPA as an optimal reference method for convergence

Abstract

We present a plane-wave (PW) implementation of the auxiliary-field quantum Monte Carlo (AFQMC) method within the projector augmented-wave (PAW) formalism in the Vienna ab initio Simulation Package (VASP). By employing an exact inversion of the PAW overlap operator, our approach maintains cubic scaling while naturally operating at the complete basis set limit defined by the PW cutoff. We benchmark this framework by calculating the equilibrium lattice constants and bulk moduli of C, BN, BP, and Si. Our analysis demonstrates that AFQMC systematically corrects the lack of long-range screening in MP2 and the missing higher-order exchange in RPA. We identify RPA as the optimal reference method due to the rapid convergence of the remaining short-range correlations with respect to supercell size. The resulting lattice constants exhibit a mean absolute relative error of 0.14 % relative to experiment, establishing the method as a rigorous benchmark tool for structural properties in condensed matter systems.