Optimization of large determinant expansions in quantum Monte Carlo

TL;DR

This paper introduces an efficient orthogonal optimization method for large CI expansions in quantum Monte Carlo, significantly reducing computational memory and statistical fluctuations, enabling rapid convergence for large wave functions.

Contribution

It develops a transcorrelated-based orthogonal optimization approach for large CI expansions in QMC, improving efficiency and reducing fluctuations compared to traditional methods.

Findings

Achieved sub-milliHartree convergence within 2-3 iterations.

Reduced statistical fluctuations by over an order of magnitude.

Successfully optimized wave functions with up to one million determinants.

Abstract

We present a new method for the optimization of large configuration interaction (CI) expansions in the quantum Monte Carlo (QMC) framework. The central idea here is to replace the non-orthogonal variational optimization of CI coefficients performed in usual QMC calculations by an orthogonal non-Hermitian optimization thanks to the so-called transcorrelated (TC) framework, the two methods yielding the same results in the limit of a complete basis set. By rewriting the TC equations as an effective self-consistent Hermitian problem, our approach requires the sampling of a single quantity per Slater determinant, leading to minimal memory requirements in the QMC code. Using analytical quantities obtained from both the TC framework and the usual CI-type calculations, we also propose improved estimators which reduce the statistical fluctuations of the sampled quantities by more than an order of magnitude. We demonstrate the efficiency of this method on wave functions containing $10^5-10^6$ Slater determinants, using effective core potentials or all-electron calculations. In all the cases, a sub-milliHartree convergence is reached within only two or three iterations of optimization.