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arXiv · 2606.00924

Locality-Induced Hierarchical Backflow Wavefunctions for Correlated Fermions

Yu-Tong Zhou·Zheng-Wei Zhou·Wen-Yuan Liu
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Abstract

We show that locality provides a natural principle to hierarchically organize backflow wavefunctions. This leads us to propose a family of variational fermionic states, termed hierarchical backflow (HB) wavefunctions. The expressive power of HB is systematically improvable, controlled by a path depth $K$ which reflects the range of backflow correlations. At half-filling, the HB with $K=1$ already achieves high energy precision, with an accuracy around $0.5\%$ for system sizes from $4\times 4$ to $10\times 10$. At hole doping $n_h=0.125$, the method scales efficiently to $12\times16$ and $16\times16$ systems, and the energy systematically achieves higher accuracy with $K$ increasing, yielding a clear stripe phase. The HB further enables a local-nonlocal decomposition, naturally bridging to neural quantum states, while featuring compact representations and efficient optimization. Our work reveals locality as a natural organizing principle of backflow wavefunctions, opening a new framework with systematic improvability and interpretability for large-scale simulations of correlated fermion systems.

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Yu-Tong Zhou, Zheng-Wei Zhou, Wen-Yuan Liu. 2026-05-30. Locality-Induced Hierarchical Backflow Wavefunctions for Correlated Fermions. https://arxiv.org/abs/2606.00924

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