{
  "abstract": "Representation learning, or featurization, of mean-field Bloch states provides an important route for incorporating electronic information into machine-learning models of first-principles condensed-phase systems. A challenge in representing Bloch states is the gauge redundancy of each state. In this work, we propose to address this issue by explicitly incorporating gauge equivariance in the machine-learning framework. We develop a $U(1)$-equivariant autoencoder that compresses the plane-wave-basis Bloch states obtained from density functional theory into a low-dimensional latent representation. We achieve an average overlap of 0.970 between original wavefunctions and the reconstructions from a 64-dimensional latent space using a dataset of two-dimensional insulators. We further show that $U(1)$ equivariance endows the latent space with physically meaningful structures, including smoothness and topological information. Finally, we present a proof-of-principle application in which the latent representations are used to predict the off-diagonal elements of the $GW$ self energy matrix, and demonstrate the importance of enforcing gauge equivariance in the prediction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30845",
  "author_total": 4,
  "authors": [
    {
      "name": "Chengyan Zhang"
    },
    {
      "name": "Xian Xu"
    },
    {
      "name": "Bowen Hou"
    },
    {
      "name": "Diana Y. Qiu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/54svhyahmny8m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30845",
  "fulltext_url": null,
  "id": "54svhyahmny8m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30845",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "2505|Machine Learning in Materials Science"
    ]
  ],
  "openalex": "W7214682139",
  "pdf_url": "https://arxiv.org/pdf/2609.30845",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/54svhyahmny8m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:52Z",
      "native_id": "2609.30845",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30845"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "$U(1)$ Gauge-Equivariant Representation Learning of Bloch States",
  "title_text": "U(1) Gauge-Equivariant Representation Learning of Bloch States",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:52Z",
  "url": "https://research.draconitic.com/paper/54svhyahmny8m",
  "venue": "arXiv",
  "versions": []
}