Yu-Tong Zhou | Searcharxiv

arXiv2026

Locality-Induced Hierarchical Backflow Wavefunctions for Correlated Fermions

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.

cond-mat.str-el↗

arXiv2024

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

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.

cond-mat.str-el↗