Solving Fermi-Hubbard-type Models by Tensor Representations of Backflow Corrections

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 model under periodic boundary conditions, current state-of-the-art methods are neural network backflows and the hidden fermion Slater determinant. The backflow correction is an efficient way to improve the Slater determinant of free-particles. In this work we propose a tensor representation of the backflow corrected wave-function, we show that for the spinless $t$-$V$ model, the energy precision is competitive or even lower than current state-of-the-art fermionic tensor network methods. For models with spin, we further improve the representation ability by considering backflows on fictitious particles with different spins, thus naturally introducing non-zero backflow corrections when the orbital and the particle have opposite spins. We benchmark our method on molecules under STO-3G basis and the Fermi-Hubbard model with periodic and cylindrical boudary conditions. We show that the tensor representation of backflow corrections achieves competitive or even lower energy results than current state-of-the-art neural network methods.