Systematic Comparison and Cross-validation of Fixed-Node Diffusion Monte Carlo and Phaseless Auxiliary-Field Quantum Monte Carlo in Solids

TL;DR

This study systematically compares fixed-node diffusion Monte Carlo and phaseless auxiliary-field quantum Monte Carlo methods in solids, highlighting their relative strengths, weaknesses, and convergence behaviors using CIPSI-generated trial wave functions.

Contribution

It provides a detailed comparison of DMC and AFQMC in solids, demonstrating their convergence and analyzing their dependence on trial wavefunctions and basis sets.

Findings

AFQMC has less trial wavefunction dependence than DMC.

Both methods converge to similar energies after correcting basis set effects.

AFQMC exhibits larger basis set dependence than DMC.

Abstract

Quantum Monte Carlo (QMC) methods are some of the most accurate methods for simulating correlated electronic systems. We investigate the compatibility, strengths and weaknesses of two such methods, namely, diffusion Monte Carlo (DMC) and auxiliary-field quantum Monte Carlo (AFQMC). The multi-determinant trial wave functions employed in both approaches are generated using the configuration interaction using a perturbative selection made iteratively (CIPSI) technique. Complete basis set full configuration interaction (CBS-FCI) energies estimated with CIPSI are used as a reference in this comparative study between DMC and AFQMC. By focusing on a set of canonical finite size solid state systems, we show that both QMC methods can be made to systematically converge towards the same energy once basis set effects and systematic biases have been removed. AFQMC shows a much smaller dependence on the trial wavefunction than DMC while simultaneously exhibiting a much larger basis set dependence. We outline some of the remaining challenges and opportunities for improving these approaches.