Efficient Neural Network Backflow Transformation for the Two-Dimensional Hubbard Model

Modeling fermionic correlations in lattice systems is challenging due to the complexity of many-body interactions. Neural network ansätze, such as backflow transformations, provide a flexible approach to capture these correlations. Here, we develop an efficient backflow neural quantum state (NQS) ansatz that substantially reduces the number of network parameters while maintaining high expressivity. Our network combines a compact transformer-style encoder with an optimized backflow neural network to represent the wave function, and we demonstrate its application to the two-dimensional Hubbard model. The architecture reformulates the backflow transformation to improve scalability with system size and enhance numerical stability.