Self-Refinement of Auxiliary-Field Quantum Monte Carlo via Non-Orthogonal Configuration Interaction

TL;DR

This paper introduces an efficient determinant selection algorithm for auxiliary-field quantum Monte Carlo that significantly reduces errors and biases, enhancing accuracy for complex molecular systems.

Contribution

We develop a novel determinant selection method that refines trial wave functions in AFQMC, substantially improving accuracy and reducing computational bias.

Findings

Error reduced by up to a factor of 10 for second row elements.

Average error improved to within chemical accuracy for the HEAT set.

Error decreased by 80% for benzene with 214 determinants.

Abstract

For optimal accuracy, auxiliary-field quantum Monte Carlo (AFQMC) requires trial states consisting of multiple Slater determinants. We develop an efficient algorithm to select the determinants from an AFQMC random walk eliminating the need for other methods. When determinants contribute significantly to the non-orthogonal configuration interaction energy, we include them in the trial state. These refined trial wave functions significantly reduce the phaseless bias and sampling variance of the local energy estimator. With 100 to 200 determinants, we lower the error of AFQMC by up to a factor of 10 for second row elements that are not accurately described with a Hartree-Fock trial wave function. For the HEAT set, we improve the average error to within the chemical accuracy. For benzene, the largest studied system, we reduce AFQMC error by 80% with 214 Slater determinants and find a 10-fold increase of the time to solution. We show that the remaining error of the method prevails in systems with static correlation or strong spin contamination.