Neuralized Fermionic Tensor Networks for Quantum Many-Body Systems

TL;DR

This paper introduces neuralized fermionic tensor network states (NN-fTNS) that enhance expressivity and computational efficiency for quantum many-body systems, demonstrated on Fermi-Hubbard models.

Contribution

The authors develop a novel neuralized fermionic tensor network framework that improves ground-state energy accuracy and computational scaling over existing methods.

Findings

Achieve order of magnitude better ground-state energies than pure fTNS at the same bond dimension.

Systematically improve results by increasing tensor network bond dimension and neural network complexity.

Construct a NN-fTNS with linear scaling in lattice size, outperforming existing fermionic neural quantum states.

Abstract

We describe a class of neuralized fermionic tensor network states (NN-fTNS) that introduce non-linearity into fermionic tensor networks through configuration-dependent neural network transformations of the local tensors. The construction uses the fTNS algebra to implement a natural fermionic sign structure and is compatible with standard tensor network algorithms, but gains enhanced expressivity through the neural network parametrization. Using the 1D and 2D Fermi-Hubbard models as benchmarks, we demonstrate that NN-fTNS achieve order of magnitude improvements in the ground-state energy compared to pure fTNS with the same bond dimension, and can be systematically improved through both the tensor network bond dimension and the neural network parametrization. Compared to existing fermionic neural quantum states (NQS) based on Slater determinants and Pfaffians, NN-fTNS offer a physically motivated alternative fermionic structure. Furthermore, compared to such states, NN-fTNS naturally exhibit improved computational scaling and we demonstrate a construction that achieves linear scaling with the lattice size.