Fermionic variational wavefunctions from neural-network constrained hidden states*

For the variational simulation of fermionic systems in first quantization, trial wavefunctions must be anti-symmetric functions of the particle configurations, while being able to capture correlations beyond the single-particle Slater determinants. This is typically achieved either by considering backflow transformations, or with Jastrow-like projection factors. Despite the recent success of neural-network based parametrizations, the strong coupling limit remains to be a challenging regime.

In this talk I will introduce a new and systematically improvable family of variational states consisting on the projection of uncorrelated Slater determinants in a Hilbert space augmented by hidden fermionic degrees of freedom. The ability to jointly optimize the single-particle orbitals together with the projection (parametrized by neural-networks) onto the physical Hilbert space, provides an extremely expressive family of wavefunction ansatze. We study the ground state properties of the Hubbard model in the square lattice, achieving levels of accuracy competitive with state-of-the-art computational methods.