{
  "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 hopping, consistent with experimental observations in cuprates. Our work establishes NQS as a powerful tool for solving challenging many-fermions systems.",
  "abstract_shown": true,
  "affiliations": [
    "ByteDance Seed, Beijing, China",
    "State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University, Beijing, China",
    "State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, China",
    "Institute of Physics, Chinese Academy of Sciences, Beijing, China",
    "Institute of Physics, Chinese Academy of Sciences, Beijing, China. yantaow@iphy.ac.cn",
    "Institute of Physics, Chinese Academy of Sciences, Beijing, China. txiang@iphy.ac.cn",
    "Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China. qinmingpu@sjtu.edu.cn",
    "State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University, Beijing, China. wanglw@pku.edu.cn",
    "ByteDance Seed, Beijing, China. ywlds163@gmail.com",
    "FieldQuantum Research Institute, Beijing, China. ywlds163@gmail.com"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 12,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Yuntian Gu",
      "orcid": "0009-0009-2720-8366"
    },
    {
      "affs": [
        0,
        1
      ],
      "name": "Wenrui Li",
      "orcid": "0000-0003-0560-3292"
    },
    {
      "affs": [
        0,
        2
      ],
      "name": "Heng Lin"
    },
    {
      "affs": [
        0,
        3
      ],
      "name": "Bo Zhan"
    },
    {
      "affs": [
        0,
        1
      ],
      "name": "Ruichen Li",
      "orcid": "0009-0003-8396-1084"
    },
    {
      "affs": [
        0
      ],
      "name": "Yifei Huang",
      "orcid": "0000-0003-4981-7452"
    },
    {
      "affs": [
        1
      ],
      "name": "Di He",
      "orcid": "0009-0003-0468-1288"
    },
    {
      "affs": [
        4
      ],
      "name": "Y N Wu",
      "orcid": "0000-0002-0833-1205"
    },
    {
      "affs": [
        5
      ],
      "name": "Tao Xiang",
      "orcid": "0000-0001-5998-7338"
    },
    {
      "affs": [
        6
      ],
      "name": "Mingpu Qin",
      "orcid": "0000-0001-7733-9684"
    },
    {
      "affs": [
        7
      ],
      "name": "Liwei Wang",
      "orcid": "0000-0003-1739-2621"
    },
    {
      "affs": [
        8,
        9
      ],
      "name": "Dingshun Lv",
      "orcid": "0000-0003-0573-6490"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fe7ns2grx3vrz.bib",
  "cited_by": 11,
  "doi": "10.1038/s41467-026-74028-6",
  "fulltext_url": null,
  "id": "fe7ns2grx3vrz",
  "issns": [
    "2041-1723"
  ],
  "landing_url": "https://doi.org/10.1038/s41467-026-74028-6",
  "language": "en",
  "licence": "CC-BY-NC-ND",
  "licence_label": "CC BY-NC-ND",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7165563151",
  "pdf_url": "https://www.nature.com/articles/s41467-026-74028-6_reference.pdf",
  "pmcid": "PMC13439271",
  "pmid": "42331803",
  "published": "2026-06-22",
  "publisher": "Nature Portfolio",
  "ris": "https://research.draconitic.com/paper/fe7ns2grx3vrz.ris",
  "sources": [
    {
      "first_seen": "2026-11-01T13:20:06Z",
      "native_id": "W7165563151",
      "source": "openalex",
      "url": "https://doi.org/10.1038/s41467-026-74028-6"
    }
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  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3107|Quantum many-body systems",
      "subfield": "amo"
    }
  ],
  "title": "Solving the Hubbard model with neural quantum states",
  "title_text": "Solving the Hubbard model with neural quantum states",
  "type": "peer-reviewed",
  "updated_at": "2026-11-05T13:20:43Z",
  "url": "https://research.draconitic.com/paper/fe7ns2grx3vrz",
  "venue": "Nature Communications",
  "versions": []
}