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

Abstract

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.

9 pages, 6 figures, comments are welcome

References in corpus (6)

• Role of backflow correlations for the non-magnetic phase of the t-t' Hubbard model
• Fermionic Wave Functions from Neural-Network Constrained Hidden States
• Stripes and spin-density waves in the doped two-dimensional Hubbard model: ground state phase diagram
• The antiferromagnetic spin-1/2 Heisenberg model on the square lattice in a magnetic field
• Coupling quantum Monte Carlo and independent-particle calculations: self-consistent constraint for the sign problem based on density or density matrix
• $2^{1296}$ Exponentially Complex Quantum Many-Body Simulation via Scalable Deep Learning Method

Cited by in corpus (2)

• Simple Fermionic backflow states via a systematically improvable tensor decomposition
• Optimizing Temperature Distributions for Training Neural Quantum States using Parallel Tempering