期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2022
卷号：119
期号：32
DOI：10.1073/pnas.2122059119
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Significance
Large systems of interacting quantum particles present a notorious computational challenge, since they require to solve an eigenvalue problem in an exponentially large dimensional space. The problem can be approached variationally: A trial wave function is proposed, depending on a set of parameters that are determined by an optimization procedure. Neural networks are a great candidate for the task as they provide an extremely flexible family of trial states. We introduce a neural-network-based trial wave function formalism for the study of systems of interacting fermions. This formalism is based on the addition of extra hidden fermions that, aided by neural networks, “mediate” the correlations between the particles in the wave function when projected back on the physical space.
We introduce a systematically improvable family of variational wave functions for the simulation of strongly correlated fermionic systems. This family consists of Slater determinants in an augmented Hilbert space involving “hidden” additional fermionic degrees of freedom. These determinants are projected onto the physical Hilbert space through a constraint that is optimized, together with the single-particle orbitals, using a neural network parameterization. This construction draws inspiration from the success of hidden-particle representations but overcomes the limitations associated with the mean-field treatment of the constraint often used in this context. Our construction provides an extremely expressive family of wave functions, which is proved to be universal. We apply this construction to the ground-state properties of the Hubbard model on the square lattice, achieving levels of accuracy that are competitive with those of state-of-the-art variational methods.
关键词：enquantum physicsneural networksvariational Monte Carloelectronic structurefermions
