Taming the sign problem in auxiliary field quantum Monte Carlo using accurate trial wave functions

TL;DR

This paper enhances auxiliary field quantum Monte Carlo by integrating accurate trial wave functions, significantly reducing the sign problem and enabling the study of larger systems with improved accuracy.

Contribution

It introduces a method to incorporate advanced trial wave functions into fp-AFQMC, improving convergence and accuracy in quantum chemical calculations.

Findings

Mitigates the sign problem in fp-AFQMC

Enables application to larger systems

Provides more accurate isomerization energies for Cu2O2^{2+}

Abstract

We explore different ways of incorporating accurate trial wave functions into free projection auxiliary field quantum Monte Carlo (fp-AFQMC). Trial states employed include coupled cluster singles and doubles, multi-Slater, and symmetry projected mean-field wave functions. We adapt a recently proposed fast multi-Slater local energy evaluation algorithm for fp-AFQMC, making the use of long expansions from selected configuration interaction methods feasible. We demonstrate how these trial wave functions serve to mitigate the sign problem and accelerate convergence in quantum chemical problems, allowing the application of fp-AFQMC to systems of substantial sizes. Our calculations on the widely studied $\text{Cu}_2\text{O}_2^{2+}$ model system show that many previously reported isomerization energies differ substantially from the near-exact fp-AFQMC value.