{
  "abstract": "We demonstrate that designing a neural quantum state to be an exact eigenstate of the Hamiltonian's symmetries significantly improves both training speed and final variational energy. For the 2D electron gas, we design TorFormer, a neural network wavefunction which is an exact eigenstate of the total momentum. TorFormer describes both the Fermi liquid and Wigner crystal with no supervision and significantly outperforms Psiformer-based references up to large system sizes. For $r_s = 30.0$ and $40.0$ at $N=91$, we compare TorFormer trained for $8\\mathrm{K}$ steps against the previous best NQS, which required $100\\mathrm{K}$ training steps. Our improvement to the total energy at $r_s = 40.0$, excluding the trivial Madelung part, is $0.12\\%$---enormous compared to the tiny differences separating phases. Relative to Slater-Jastrow-backflow diffusion Monte Carlo, TorFormer's energy decrease is roughly $9.8$ times that of the previous best NQS. Our work demonstrates that neural quantum states can both accurately and efficiently solve large-scale problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10186",
  "author_total": 3,
  "authors": [
    {
      "name": "David D. Dai"
    },
    {
      "name": "Yen-Ting Lin"
    },
    {
      "name": "Marin Soljačić"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7g6ba5hd03tyz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10186",
  "fulltext_url": null,
  "id": "7g6ba5hd03tyz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10186",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7212134628",
  "pdf_url": "https://arxiv.org/pdf/2609.10186",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7g6ba5hd03tyz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.10186",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10186"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Fast, Accurate, and Scalable Fermionic Neural Networks via Translation Equivariance",
  "title_text": "Fast, Accurate, and Scalable Fermionic Neural Networks via Translation Equivariance",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:12Z",
  "url": "https://research.draconitic.com/paper/7g6ba5hd03tyz",
  "venue": "arXiv",
  "versions": []
}