Revisiting Backflow Corrections by Tensor Representations: Benchmarks on Fermi-Hubbard-type Models

• URL: http://arxiv.org/abs/2308.11823v5
• Date: Tue, 19 Mar 2024 15:18:17 GMT
• Title: Revisiting Backflow Corrections by Tensor Representations: Benchmarks on Fermi-Hubbard-type Models
• Authors: Yu-Tong Zhou, Zheng-Wei Zhou, Xiao Liang,
• Abstract summary: We show that our methods achieve competitive or even lower energy results than current state-of-the-art methods. We benchmark on molecules under STO-3G basis and the Fermi-Hubbard model with periodic and cylindrical boudary conditions.
• Score: 5.256608661803256
• License: http://creativecommons.org/licenses/by/4.0/
• 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, 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 tensor network methods. For models with spin, we further improve the representation ability by considering non-zero backflow corrections on different spins between the orbital and the particle. We benchmark on molecules under STO-3G basis and the Fermi-Hubbard model with periodic and cylindrical boudary conditions. We show that our methods achieve competitive or even lower energy results than current state-of-the-art methods.

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