Neural Transformer Backflow for Solving Momentum-Resolved Ground States of Strongly Correlated Materials

Abstract

Strongly correlated materials host a rich variety of exotic quantum phases but remain challenging to solve due to strong interactions. We introduce the Neural Transformer Backflow (NTB) framework, a powerful neural-network ansatz formulated within a multi-band projection formalism. NTB is mean-field transcendental, parameter-efficient and fermionic intrinsic, exhibiting superior performance compared with existing neural ansatzes. By naturally enforcing momentum conservation, NTB enables direct computation of momentum-resolved many-body ground states, providing detailed access to degeneracies and energy gaps. It achieves high accuracy on small systems and scales efficiently to larger sizes and higher-band truncations far beyond the reach of exact diagonalization. We demonstrate the power of NTB in capturing diverse correlated phases in twisted MoTe$_2$, including charge density waves, fractional Chern insulators, and anomalous Hall Fermi liquids, within a unified framework. This approach offers a generic, scalable route towards understanding and discovering quantum phases in strongly correlated materials.