Investigating the crust of neutron stars with neural-network quantum states

TL;DR

This paper introduces a neural-network-based variational Monte Carlo method to microscopically model the transition from neutron-rich nuclei to uniform liquid in neutron star crusts, overcoming previous computational limitations.

Contribution

It presents a novel neural Pfaffian-Jastrow quantum state approach that improves upon existing methods for low-density nuclear matter simulations, capturing cluster formation.

Findings

Nuclear clusters dynamically emerge at low densities.

The method accurately computes energy per particle for nuclear matter.

Cluster presence affects proton distribution in the crust.

Abstract

An accurate description of low-density nuclear matter is crucial for explaining the physics of neutron star crusts. In the density range between approximately 0.01 fm$^{-3}$ and 0.1 fm$^{-3}$, matter transitions from neutron-rich nuclei to various higher-density pasta shapes, before ultimately reaching a uniform liquid. In this work, we introduce a variational Monte Carlo method based on a neural Pfaffian-Jastrow quantum state, which allows us to model the transition from the liquid phase to neutron-rich nuclei microscopically. At low densities, nuclear clusters dynamically emerge from the microscopic interactions among protons and neutrons, which we model based on pionless effective field theory. Our variational Monte Carlo approach represents a significant improvement over the state-of-the-art auxiliary-field diffusion Monte Carlo method, which is severely hindered by the fermion-sign problem in this low-density regime and cannot capture the onset of clusters. In addition to computing the energy per particle of symmetric nuclear matter and pure neutron matter, we analyze an intermediate isospin-asymmetry configuration to elucidate the formation of nuclear clusters. We also provide evidence that the presence of such nuclear clusters influences the amount of protons in the crust compared to protons in beta-equilibrated, neutrino-transparent matter.