Restricted Boltzmann Machines Propagators for Auxiliary Field Diffusion Monte Carlo

TL;DR

This paper introduces a novel representation of the imaginary-time propagator in auxiliary field diffusion Monte Carlo using restricted Boltzmann machines, enabling more realistic nuclear potential modeling.

Contribution

The work presents a new RBM-based propagator for auxiliary field diffusion Monte Carlo, improving the accuracy and potential for complex nuclear interactions.

Findings

RBM propagator matches traditional methods in accuracy

Tested on light nuclei ground-state energies and densities

Enables inclusion of advanced nuclear potentials

Abstract

The auxiliary field diffusion Monte Carlo method uses imaginary-time projection techniques to accurately solve the ground-state wave function of atomic nuclei and infinite nuclear matter. In this work, we present a novel representation of the imaginary-time propagator based on restricted Boltzmann machines. We test its accuracy against the routinely employed Hubbard-Stratonovich transformations by evaluating ground-state energies and single-particle densities of selected light nuclei. This analysis paves the way for incorporating more realistic nuclear potentials in the auxiliary field diffusion Monte Carlo method, including isospin-dependent spin-orbit terms and cubic spin-isospin operators, which characterize accurate phenomenological and chiral effective field theory Hamiltonians.