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