Solving the Hubbard model with Neural Quantum States
This work provides a powerful tool for solving challenging many-fermion quantum systems, with implications for understanding high-temperature superconductivity in materials like cuprates, though it is incremental in advancing neural quantum states.
The authors tackled the doped two-dimensional Hubbard model, a key model for high-Tc superconductivity, by using transformer-based neural quantum states and achieved state-of-the-art results, including establishing the half-filled stripe ground state consistent with experimental observations in cuprates.
The rapid development of neural quantum states (NQS) has established it as a promising framework for studying quantum many-body systems. In this work, by leveraging the cutting-edge transformer-based architectures and developing highly efficient optimization algorithms, we achieve the state-of-the-art results for the doped two-dimensional (2D) Hubbard model, arguably the minimum model for high-Tc superconductivity. Interestingly, we find different attention heads in the NQS ansatz can directly encode correlations at different scales, making it capable of capturing long-range correlations and entanglements in strongly correlated systems. With these advances, we establish the half-filled stripe in the ground state of 2D Hubbard model with the next nearest neighboring hoppings, consistent with experimental observations in cuprates. Our work establishes NQS as a powerful tool for solving challenging many-fermions systems.