Perturbative quantum Monte Carlo method for nuclear physics

TL;DR

This paper introduces a novel perturbative quantum Monte Carlo method that efficiently computes higher-order corrections for nuclear ground states, overcoming numerical challenges and applicable across various many-body systems.

Contribution

The authors develop a new approach for perturbative corrections in projection QMC, enabling accurate second-order energy calculations for nuclei without the sign problem.

Findings

Good agreement with experimental nuclear binding energies

Large second order energy corrections due to symmetry breaking

Method is free from the sign problem and broadly applicable

Abstract

While first order perturbation theory is routinely used in quantum Monte Carlo (QMC) calculations, higher-order terms present significant numerical challenges. We present a new approach for computing perturbative corrections in projection QMC calculations. We demonstrate the method by computing nuclear ground state energies up to second order for a realistic chiral interaction. We calculate the binding energies of several light nuclei up to $^{16}$O by expanding the Hamiltonian around the Wigner SU(4) limit and find good agreement with data. In contrast to the natural ordering of the perturbative series, we find remarkably large second order energy corrections. This occurs because the perturbing interactions break the symmetries of the unperturbed Hamiltonian. Our method is free from the sign problem and can be applied to QMC calculations for many-body systems in nuclear physics, condensed matter physics, ultracold atoms, and quantum chemistry.