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

TL;DR

This review discusses how artificial neural network representations of the nuclear many-body wave function have significantly extended the capabilities of continuum quantum Monte Carlo methods, and highlights developments in neural network quantum states that bridge strongly correlated systems across disciplines.

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.

Figures (34)

• Figure 2.1: Phase shifts in the $^3S_1$ and $^1S_0$ channels for $np$ scattering computed using the LO EFT Hamiltonian "o" of Ref. schiavilla_two-_2021, compared to the PWA93 analysis and results from the realistic Argonne v$_{18}$ potential wiringa_accurate_1995.
• Figure 2.2: Phase shifts in the $^1S_0$ channels for $pp$ and $nn$ scattering computed using the LO EFT Hamiltonian "o" of Ref. schiavilla_two-_2021 compared to the PWA93 analysis and results from the realistic Argonne v$_{18}$ potential wiringa_accurate_1995..
• Figure 2.3: Radial functions of the model "o" $N\!N$ potential at LO in the pionless EFT expansion, expressed in the spin--isospin basis.
• Figure 2.4: Radial functions of the Argonne $v_8^\prime$ potential, expressed in the spin–isospin basis.
• Figure 2.5: Number of many-body spin--isospin states, $2^A \binom{A}{Z}$, relevant to VMC and GFMC calculations for selected light nuclei.