Perturbative quantum Monte Carlo calculation with high-fidelity nuclear forces

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.