Neural Network Backflow with Low-Rank Multi-Determinant Updates
Abstract
Simulating strongly correlated fermions remains a long-standing challenge due to the exponential complexity of the Hilbert space and the intricate sign structure of many-body wavefunctions. We introduce a variational framework centered on a neural network backflow transformation that combines deep learning with variational Monte Carlo. The proposed ansatz employs a multi-determinant expansion with low-rank shifts to capture non-local correlations and complex sign structures. Applied to the two-dimensional Hubbard model at both half-filling and 1/8 doping, the method achieves energies within 0.45% of auxiliary-field quantum Monte Carlo at half-filling and captures intertwined charge- and spin-density stripe patterns at 1/8 doping. These results demonstrate the potential of this framework as a scalable and interpretable approach to variational simulations of strongly correlated fermionic systems.
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BibTeX
@misc{huang2026neural,
title = {{Neural Network Backflow with Low-Rank Multi-Determinant Updates}},
author = {Tianshu Huang and Xiaowei Ou and Vidvuds Ozolins},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26544},
eprint = {2609.26544},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26544},
}
RIS
TY - UNPB
TI - Neural Network Backflow with Low-Rank Multi-Determinant Updates
AU - Tianshu Huang
AU - Xiaowei Ou
AU - Vidvuds Ozolins
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26544
UR - https://arxiv.org/abs/2609.26544
AB - Simulating strongly correlated fermions remains a long-standing challenge due to the exponential complexity of the Hilbert space and the intricate sign structure of many-body wavefunctions. We introduce a variational framework centered on a neural network backflow transformation that combines deep learning with variational Monte Carlo. The proposed ansatz employs a multi-determinant expansion with low-rank shifts to capture non-local correlations and complex sign structures. Applied to the two-dimensional Hubbard model at both half-filling and 1/8 doping, the method achieves energies within 0.45% of auxiliary-field quantum Monte Carlo at half-filling and captures intertwined charge- and spin-density stripe patterns at 1/8 doping. These results demonstrate the potential of this framework as a scalable and interpretable approach to variational simulations of strongly correlated fermionic systems.
ER -