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

TL;DR

This paper introduces a tensor-based approach to backflow corrections in wave-functions, achieving competitive or superior energy accuracy for Fermi-Hubbard models and molecules compared to existing neural network methods.

Contribution

It proposes a novel tensor representation of backflow-corrected wave-functions, enhancing the modeling of fermionic systems with spin and boundary conditions.

Findings

Tensor representation achieves lower or comparable energy accuracy.

Method outperforms neural network approaches in benchmark tests.

Effective for both spinless and spinful fermionic models.

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.