# Solving the Hubbard model with Neural Quantum States

arXiv: https://arxiv.org/abs/2507.02644 · HTML: https://mlsanity.com/paper/2507.02644/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2025.

## Built on by (most cited first, 5 of 5)

- [A Sketch-and-Project Analysis of Subsampled Natural Gradient Algorithms](https://mlsanity.com/paper/2508.21022/) (2025)
- [Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo](https://mlsanity.com/paper/2605.13807/) (2026)
- [Reduced Density Matrices Through Machine Learning](https://mlsanity.com/paper/2511.07367/) (2025)
- [Fermionic neural Gibbs states](https://mlsanity.com/paper/2512.04663/) (2025)
- [Representability-Aware Neural Networks for Reduced Density Matrices: Application to Fractional Chern Insulators](https://mlsanity.com/paper/2605.20326/) (2026)

## Abstract (arXiv)

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.