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.

Strongly Correlated Electrons (cond-mat.str-el); Superconductivity (cond-mat.supr-con); Quantum Physics (quant-ph)

arXiv:2609.26544 [cond-mat.str-el]

(or arXiv:2609.26544v1 [cond-mat.str-el] for this version)

https://doi.org/10.48550/arXiv.2609.26544 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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