Solving the Hubbard model with Neural Quantum States

TL;DR

This paper demonstrates that neural quantum states, enhanced with transformer architectures and efficient algorithms, can accurately model the 2D Hubbard model, capturing complex correlations and reproducing experimental phenomena.

Contribution

It introduces advanced transformer-based neural quantum states and optimization methods, achieving state-of-the-art results for the 2D Hubbard model and revealing insights into long-range correlations.

Findings

Achieved state-of-the-art results for the doped 2D Hubbard model.

Found that attention heads encode correlations at different scales.

Reproduced the half-filled stripe in the ground state consistent with experiments.

Abstract

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.