ArticleNature communications2026
Solving the Hubbard model with neural quantum states.
Article in Nature communications, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. An erratum has been issued. Cited by 1 paper.
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Who cites it
1 citing paper in PubMed.
- Implicitly Restarted Lanczos Enables Chemically Accurate Shallow Neural Quantum States.Precision chemistry · 2026Article
Corrections and comments
- Erratum issued
Authors and funding
12 authors.
Funding
No grant is acknowledged in the PubMed record.
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 transformer-based architectures and developing 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 in strongly correlated systems. With these advances, we find evidence for the half-filled stripe in the ground state of 2D Hubbard model with the next nearest neighboring hopping, consistent with experimental observations in cuprates. Our work establishes NQS as a powerful tool for solving challenging many-fermions systems.
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Registered trials
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