Spin-adapted neural network backflow for strongly correlated electrons

TL;DR

This paper introduces a spin-adapted neural network backflow method that maintains spin symmetry in strongly correlated electron systems, enabling accurate and efficient quantum simulations.

Contribution

The authors develop a novel spin-adapted neural network backflow ansatz with tensor compression and particle-hole duality, improving accuracy and computational efficiency in quantum chemistry.

Findings

Outperforms standard neural network backflow in molecular systems.

Achieves higher accuracy than spin-adapted DMRG for FeMoco.

Enables simulations of systems with over 100 electrons.

Abstract

Accurately describing strongly correlated electrons in systems such as transition metal complexes requires strict adherence to spin symmetry, a feature largely absent in modern neural-network-based variational wavefunctions. This deficiency can lead to severe spin contamination in simulating systems with near-degenerate spin states. To resolve this limitation, we present a spin-adapted neural network backflow (SA-NNBF) ansatz, formulated in second quantization for fermionic lattice models and ab initio quantum chemistry. Our approach constructs a fully antisymmetric wavefunction by combining a neural-network backflow spatial component with a spin eigenfunction expressed in a sum-of-products form. To address the computational complexity of spin adaptation, we introduce a tensor compression algorithm for spin eigenfunctions, and a more compact wavefunction representation based on the particle-hole duality in second quantization. These advancements enable variational Monte Carlo calculations using SA-NNBF for challenging molecular systems with more than one hundred electrons, including the FeMo-cofactor (FeMoco) in nitrogenase. Applications to prototypical strongly correlated molecules demonstrate that SA-NNBF consistently outperforms standard NNBF with a similar number of parameters. Furthermore, it surpasses the accuracy of the state-of-the-art spin-adapted density matrix renormalization group (SA-DMRG) algorithm for FeMoco with a significantly reduced computational resource. Our work establishes a foundational framework for exploring fully symmetry-preserving neural-network quantum states for interacting fermion problems.