Efficient local energy evaluation for multi-Slater wave functions in orbital space quantum Monte Carlo

TL;DR

This paper introduces an efficient algorithm for calculating the local energy of multi-Slater wave functions in orbital space QMC, significantly reducing computational cost and enabling larger configuration spaces.

Contribution

The authors develop a new $O(n^5 + n_c)$ scaling algorithm for local energy evaluation in orbital space QMC, improving over previous methods and allowing larger wave functions.

Findings

Reduced computational scaling from $O(n^4 n_c)$ to $O(n^5 + n_c)$

Demonstrated application to polyacetylene with larger configuration sets

Potential applicability to auxiliary field quantum Monte Carlo

Abstract

Recent developments in selected configuration interaction methods have led to increased interest in using multi-Slater trial wave functions in various quantum Monte Carlo (QMC) methods. Here we present an algorithm for calculating the local energy of a multi-Slater wave function in orbital space QMC. For an ab initio Hamiltonian, our algorithm has a cost scaling of $O(n^5 + n_c)$, as opposed to the $O(n^4n_c)$ scaling of existing orbital space algorithms, where $n$ is the system size, and $n_c$ is the number of configurations in the wave function. We present our method using variational Monte Carlo calculations with the Jastrow multi-Slater wave function, although the formalism should be applicable for auxiliary field quantum Monte Carlo. We apply it to polyacetylene and demonstrate the possibility of using a much larger number of configurations than possible using existing methods.