Sign-Problem-Free Nuclear Quantum Monte Carlo Simulation

Abstract

Quantum Monte Carlo (QMC) methods offer exact solutions for quantum many-body systems but face severe limitations in fermionic systems like atomic nuclei due to the sign problem. While sign-problem-free QMC algorithms exist and provide valuable insights across disciplines, they have been restricted to simple models with limited quantitative predictive power. Here we overcome this barrier by developing a novel lattice nuclear force that is rigorously sign-problem-free for even-even nuclei. This interaction achieves a standard deviation of $\sigma = 2.932$ MeV from experimental binding energies for 76 even-even nuclei ($N,Z \leq 28$), matching state-of-the-art phenomenological mean-field models. Key innovations include the first sign-problem-free implementation of spin-orbit coupling for shell evolutions and an efficient QMC-optimized framework for global parameter fitting. Using this approach, we compute binding energies from $^4$He to $^{132}$Sn with unprecedented one-thousandth level numerical precision, reproduce symmetric nuclear matter saturation, and reveal novel spin-orbit-driven clustering in light nuclei. This work transforms sign-problem-free QMC into a scalable and predictive nuclear structure tool, while establishing a high-fidelity, non-perturbative foundation for \textit{ab initio} calculations of heavy nuclei.