2025/07/02 by Liang, Xiao
#FOS: Physical sciences #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2507.01856
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× 16 lattice under periodoc boundary condition. For a similar case under open boundary condition, obtained energy is only 4.5× 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× 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× 12 lattice under PBC is 8.1× 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.