Neural quantum states in condensed matter: advances, best practices, and prospects

Abstract:Neural quantum states provide flexible variational representations of quantum many-body wave functions by combining neural-network parametrizations with Monte Carlo sampling. In this perspective, we review recent advances in their application to condensed-matter systems, focusing on frustrated quantum magnets, interacting lattice fermions, and non-equilibrium dynamics. We discuss the architectures, symmetry constraints, optimization methods, and sampling strategies underlying state-of-the-art calculations, and summarize practical guidelines for reliable simulations. We also examine the principal remaining challenges, including learning non-trivial sign and phase structures, controlling variational bias, enforcing physical symmetries, scaling optimization to large networks, and achieving stable real-time evolution. Finally, we outline promising directions in which neural quantum states may extend the reach of classical simulations of strongly correlated quantum matter.

Strongly Correlated Electrons (cond-mat.str-el); Computational Physics (physics.comp-ph); Quantum Physics (quant-ph)

arXiv:2608.21291 [cond-mat.str-el]

(or arXiv:2608.21291v1 [cond-mat.str-el] for this version)

https://doi.org/10.48550/arXiv.2608.21291 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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