{
  "abstract": "Most existing equivariant architectures for Hamiltonian prediction propagate features in direct-sum spaces of irreducible spherical tensors, whereas the target Hamiltonian is naturally an operator block in a direct-product representation over local orbital and spin bases. This representation mismatch fragments contiguous Hamiltonian blocks, obscures direct manipulation of orbital couplings, and organizes features into irregular angular-momentum components that require numerous transformations and are poorly aligned with efficient hardware execution and memory management. To address both the representation mismatch and computational bottleneck, we propose DP-Learner, an equivariant learning framework that performs message passing directly on Hamiltonian-like operator blocks in the direct-product space. Theoretically, we propose Lie-generator-based directional embedding and invariantly weighted left--right products and contractions that preserve equivariance to SO(3), SU(2), and spatial inversions, without explicit Clebsch--Gordan decomposition or inverse reconstruction. Methodologically, we instantiate this principle as a Transformer architecture, in which Hamiltonian-like feature matrices or tensors evolve through equivariant operators in the direct-product space, while non-linear invariant scalar routing controls structured gating over matrix units, directional propagation, attention, and environment-embedded context interactions. We further construct MP-HAM-110K, a large-scale Hamiltonian dataset comprising more than 110,000 material structures covering 68 elements with both Hamiltonian and wavefunction data. Experiments on MP-HAM-110K and Materials-HAM-SOC demonstrate that DP-Learner dramatically improves Hamiltonian prediction accuracy and inference efficiency over the state-of-the-art method.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07695",
  "author_total": 4,
  "authors": [
    {
      "name": "Shi Yin"
    },
    {
      "name": "Zujian Dai"
    },
    {
      "name": "Xinyang Pan"
    },
    {
      "name": "Lixin He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7xx2rfxc7n9bn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07695",
  "fulltext_url": null,
  "id": "7xx2rfxc7n9bn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07695",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ],
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07695",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7xx2rfxc7n9bn.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:30Z",
      "native_id": "2611.07695",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07695"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Equivariant Deep Learning in Direct-Product Space for Electronic-Structure Hamiltonian Prediction",
  "title_text": "Equivariant Deep Learning in Direct-Product Space for Electronic-Structure Hamiltonian Prediction",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:41Z",
  "url": "https://research.draconitic.com/paper/7xx2rfxc7n9bn",
  "venue": "arXiv",
  "versions": []
}