Second-Order Perturbation Theory in Continuum Quantum Monte Carlo Calculations

Abstract

We report on the first results for the second-order perturbation theory correction to the ground-state energy of a nuclear many-body system in a continuum quantum Monte Carlo calculation. Second-order (and higher) perturbative corrections are notoriously difficult to compute in most \textit{ab~initio} many-body methods, where the focus is usually on obtaining the ground-state energy. By mapping our calculation of the second-order energy correction to an evolution in imaginary time using the diffusion Monte Carlo method, we are able to calculate these corrections for the first time. After benchmarking our method in the few-body sector, we explore the effect of charge-independence breaking terms in the nuclear Hamiltonian. We then employ the new approach to investigate the many-body, perturbative, order-by-order convergence that is fundamental in modern theories of the nucleon-nucleon interaction derived from chiral effective field theory. Our approach is quite general and promises to be of wide applicability.Comment: 6 pages, 3 figures, 1 tabl