📝 SummarXiv

Abstract

We apply the Tensor-Backflow method to investigate the Fermi-Hubbard model on two-dimensional lattices as large as 256 sites, under various interaction strengths $U$, electron fillings $n$, next-nearest-neighbor hopping strengths $t'$ and boundary conditions. Instead of considering backflow terms from all sites, competitive results are achieved by considering nearest-neighbor or next-nearest-neighbor backflow terms. Meanwhile the variational wave-function is not enforced on geometric symmetries. When $t'$=0, by considering nearest-neighbor backflow terms, linear stripe order is sucessfully obtained for the case of $n$=0.875 and $U$=8 on the $16\times 16$ lattice under periodoc boundary condition. For a similar case under open boundary condition, obtained energy is only $4.5\times 10^{-4}$ higher than the state-of-the-art method fPEPS with the bond dimension $D$=20. Comparing to state-of-the-art neural network results, energies are competitive and relative errors are below $5\times 10^{-3}$. For cases of $n$=0.8 and 0.9375, results consistent with the phase diagram from AFQMC are obtained by direct optimizations. When $t'$=-0.2, by considering next-nearest-neighbor backflow terms, obtained energies are competitive or even lower than state-of-the-art neural network results. For example, obtained energy for $n$=0.875, $U$=8 on the $12\times 12$ lattice under PBC is $8.1\times 10^{-4}$ lower comparing to that from the neural network state. Therefore, the Tensor-Backflow method has strong representation abilities for the Fermi-Hubbard model.