Second-Order Perturbation Theory in Continuum Quantum Monte Carlo Calculations

TL;DR

This paper introduces a novel quantum Monte Carlo method to compute second-order perturbation corrections in nuclear many-body systems, revealing important insights into the perturbative nature of chiral nuclear potentials.

Contribution

The authors develop and benchmark a new approach to calculate second-order energy corrections in continuum quantum Monte Carlo, enabling analysis of perturbation theory in nuclear physics.

Findings

Identified cutoff-dependent perturbativeness at higher chiral orders

Discovered nonperturbative differences between leading and next-to-leading order potentials

First calculation of second-order energy correction in continuum quantum Monte Carlo

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 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 nuclear 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 that 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. We find cutoff-dependent perturbativeness between potentials at higher chiral order and also that the difference between leading order and next-to-leading order potentials is nonperturbative; both of these results have important implications for future nuclear many-body calculations. Our approach is quite general and promises to be of wide applicability.