{
  "abstract": "Developing accurate numerical methods for strongly interacting fermions is crucial for improving our understanding of various quantum many-body phenomena, especially unconventional superconductivity. Recently, neural quantum states have emerged as a promising approach for studying correlated fermions, highlighted by the hidden fermion and backflow methods, which use neural networks to model corrections to fermionic quasiparticle orbitals. In this work, we expand these ideas to the space of Pfaffians, a wave-function that naturally expresses superconducting pairings, and propose the hidden fermion Pfaffian state (HFPS), which flexibly represents both unpaired and superconducting phases and scales to large systems with favorable asymptotic complexity. In our numerical experiments, HFPS provides state-of-the-art variational accuracy in different regimes of both the attractive and repulsive Hubbard models. We show that the HFPS is able to capture general phases with and without pairing, and therefore may be a useful tool for modeling phases with unconventional superconductivity.",
  "abstract_shown": true,
  "affiliations": [
    "Center for Computational Quantum Physics, Flatiron Institute",
    "Division of Chemistry and Chemical Engineering, California Institute of Technology",
    "Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg",
    "Center for Computational Mathematics, Flatiron Institute",
    "Department of Physics and Astronomy, Rutgers University",
    "Centre de Physique Théorique, CNRS, École Polytechnique, IP Paris",
    "Collège de France",
    "Department of Quantum Matter Physics, Université de Genève"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "affs": [
        0,
        1,
        2
      ],
      "name": "Ao Chen"
    },
    {
      "affs": [
        0
      ],
      "name": "Zhou‐Quan Wan",
      "orcid": "0009-0007-6260-8715"
    },
    {
      "affs": [
        3,
        0,
        4
      ],
      "name": "Anirvan M. Sengupta",
      "orcid": "0000-0002-1080-0744"
    },
    {
      "affs": [
        0,
        5,
        6,
        7
      ],
      "name": "Antoine Georges",
      "orcid": "0000-0001-9479-9682"
    },
    {
      "affs": [
        0
      ],
      "name": "Christopher Roth"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8k766ghv19abr.bib",
  "cited_by": 36,
  "doi": "10.1073/pnas.2535288123",
  "fulltext_url": null,
  "id": "8k766ghv19abr",
  "issns": [
    "0027-8424",
    "1091-6490"
  ],
  "landing_url": "https://doi.org/10.1073/pnas.2535288123",
  "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": "W4414943256",
  "pdf_url": null,
  "pmcid": "PMC13535181",
  "pmid": "42664040",
  "published": "2026-08-28",
  "publisher": "National Academy of Sciences",
  "ris": "https://research.draconitic.com/paper/8k766ghv19abr.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T13:20:44Z",
      "native_id": "W4414943256",
      "source": "openalex",
      "url": "https://doi.org/10.1073/pnas.2535288123"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3107|Quantum many-body systems",
      "subfield": "amo"
    }
  ],
  "title": "Neural network–augmented Pfaffian wave-functions for scalable simulations of interacting fermions",
  "title_text": "Neural network–augmented Pfaffian wave-functions for scalable simulations of interacting fermions",
  "type": "peer-reviewed",
  "updated_at": "2026-11-08T13:20:37Z",
  "url": "https://research.draconitic.com/paper/8k766ghv19abr",
  "venue": "Proceedings of the National Academy of Sciences",
  "versions": []
}