Neural quantum states for strongly correlated fermions

Abstract: Strongly correlated quantum systems pose a central challenge across nuclear, atomic, and condensed-matter physics: their collective behavior emerges from interactions that are too strong and complex for mean-field or perturbative approaches, and their many-body wave functions live in exponentially large spaces. In this talk, I will introduce neural quantum states (NQS) as a flexible variational framework for representing and optimizing many-body wave functions in fermionic systems with both continuous and discrete degrees of freedom. After briefly reviewing the variational Monte Carlo method, I will show how modern neural-network architectures can encode high-dimensional correlations, fermionic antisymmetry, and physical symmetries directly into the wave function ansatz. I will then highlight recent applications of NQS to strongly correlated systems, including ultracold Fermi gases, neutron-star matter, and atomic nuclei. These examples illustrate how a common computational framework can describe pairing, clustering, and long-range correlations across traditionally separate subfields.