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

Abstract: Strongly correlated materials, such as twisted transition-metal dichalcogenide homobilayers, host a variety of exotic quantum phases but remain notoriously difficult to solve due to strong interactions. We introduce a powerful neural network ansatz, Neural Transformer Backflow (NTB), formulated within a multi-band projection framework. It naturally enforces momentum conservation and enables efficient calculations of momentum-resolved ground states. NTB attains high accuracy on small systems and scales to higher bands and larger system sizes far beyond the reach of exact diagonalization. By evaluating observables such as the structure factor and momentum distribution, we show that NTB captures diverse correlated states in tMoTe$_2$, including charge density waves, fractional Chern insulators, and anomalous Hall Fermi liquids, within a unified framework. Our approach paves the way for understanding and discovering novel phases of matter in strongly correlated materials.