Spectroscopy of two-dimensional interacting lattice electrons using symmetry-awareneural backflow transformations*

Neural networks have shown to be a powerful tool to represent many-body states, including for

fermionic systems. In this paper, we introduce a framework for embedding lattice symmetries in

Slater-Backflow-Jastrow wavefunction ansatze, and demonstrate how our model allows us to map the

ground state and low-lying excited states. To capture the Hamiltonian symmetries, we introduce

group-equivariant backflow transformations. We benchmark our ansatz on the t-V model on a

squared lattice and find that it significantly decreases the relative error when searching for ground

states, and accurately accesses low-lying excited states.In addition, our ansatz is able to compute

other observables such as the two-point-density correlation function and the structure factor in

order to detect the phase transiton critical point. Finally, we quantify the variational accuracy of

the model with the V-score.