Backflow Corrections of Green's Functions: Benchmarks on the Two-dimensional Fermi-Hubbard-type Model

The quantum many-body problem is an important topic in condensed matter physics. To efficiently solve the problem, several methods have been developped to improve the representation ability of wave-functions. For the Fermi-Hubbard-type model, the ground energy contains one-body and two-body correlations. In contrast to the wave-function, the Green function directly represents the spatio-temporal correlations between multiple sites. In this work, we propose a backflow correction of the one-body Green function to improve the ability to capture correlations. Our method is benchmarked on the spinless t−V model with open boundary conditions and on the Fermi-Hubbard model with periodic and cylindrical boudary conditions, both on rectangular lattices. The energies achieved by our method are competitive with or even lower than those achieved by state-of-the-art methods.