Neural-network quantum states for the nuclear many-body problem

TL;DR

This paper reviews how neural network quantum states enhance nuclear many-body calculations, enabling larger system simulations and capturing complex phenomena like clustering and superfluidity, thus advancing nuclear theory.

Contribution

It introduces neural network quantum states as a flexible tool that extends continuum quantum Monte Carlo methods for nuclear systems, improving accuracy and scope.

Findings

Neural network quantum states enable larger system simulations.

They effectively capture nuclear clustering and superfluid phenomena.

Applications include finite nuclei and dense nuclear matter.

Abstract

A long-standing goal of nuclear theory is to explain how the structure and dynamics of atomic nuclei and neutron-star matter emerge from the underlying interactions among protons and neutrons. Achieving this goal requires solving the nuclear quantum many-body problem with high accuracy across a wide range of length scales and density regimes. In this review, we discuss how artificial neural network representations of the nuclear many-body wave function have significantly extended the capabilities of continuum quantum Monte Carlo methods. In particular, neural network quantum states enable calculations of larger systems than were previously accessible and provide a flexible framework for capturing phenomena that challenge conventional approaches, including the emergence of nuclear clusters and superfluid phases in dense matter. We highlight recent applications to finite nuclei, infinite nuclear and neutron matter, and dynamical processes relevant to lepton-nucleus and nucleus-nucleus scattering. We also discuss conceptual and methodological connections with condensed matter physics, emphasizing developments in neural network quantum states that bridge strongly correlated systems across disciplines. Together, these developments demonstrate how neural-network methods open new avenues toward unified and accurate descriptions of nuclear structure, matter, and reactions.