Perturbative quantum Monte Carlo calculation with high-fidelity nuclear forces

TL;DR

This paper introduces a perturbative quantum Monte Carlo method for high-precision nuclear force calculations, successfully applying it to complex chiral interactions and benchmarking against known solutions to advance io nuclear structure modeling.

Contribution

It presents the first application of perturbative QMC to N$^3$LO chiral forces, demonstrating its effectiveness and hierarchical simplification in nuclear many-body calculations.

Findings

Accurate perturbative energies up to second order for chiral forces.

Benchmarking results for deuteron match exact solutions.

Reproduction of the Tjon line correlating different nuclear binding energies.

Abstract

Quantum Monte Carlo (QMC) is a family of powerful tools for addressing quantum many-body problems. However, its applications are often plagued by the fermionic sign problem. A promising strategy is to simulate an interaction without sign problem as the zeroth order and treat the other pieces as perturbations. According to this scheme, we construct precision nuclear chiral forces on the lattice and make perturbative calculations around a sign-problem-free interaction respecting the Wigner-SU(4) symmetry. We employ the recently developed perturbative QMC (ptQMC) method to calculate the perturbative energies up to the second order. This work presents the first ptQMC calculations for two-body next-to-next-to-next-to leading order (N$^3$LO) chiral forces and elucidates how the hierarchical nature of the chiral interactions helps organize and simplify the ptQMC calculations. We benchmark the algorithm for the deuteron, where exact solutions serve as rigorous reference points. We also reproduce the famous Tjon line by correlating the perturbative $^{4}$He binding energies with the non-perturbative $^{3}$H binding energies. These comprehensive demonstrations underscore the efficacy of ptQMC in resolving high-fidelity nuclear interactions, establishing its potential as a robust tool for \textit{ab initio} nuclear structure studies.