{
  "abstract": "In the Path Integral Monte Carlo (PIMC) simulation of fermions in a harmonic trap, with and without pairwise harmonic interactions, the partition functions for any discrete number of imaginary time slices (or beads) and for any choice of the short-time propagator can be analytically obtained from the contracted determinant form of the propagator. This work shows that the resulting recursion relation can be reformulated in the $λ$-ring language, yielding a closed-form finite-bead partition function in two dimensions in terms of permutation statistics. This closed-form partition function can be evaluated by a special algorithm in $O(n^2)$ time, providing an exact and numerically stable scheme for reproducing the energies of the original (undoable) fermion PIMC simulation for $n=10^4$ or more fermions. This result provides a concrete framework in which the numerical instability of the sign problem is completely bypassed, and serves as a counterexample to the prevailing view that all truly fermionic PIMC sign problems are NP-hard.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09071",
  "author_total": 3,
  "authors": [
    {
      "name": "Aarif Chaudhary"
    },
    {
      "name": "Jonas Valenzuela"
    },
    {
      "name": "Siu A. Chin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2dtb2hchggmpq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09071",
  "fulltext_url": null,
  "id": "2dtb2hchggmpq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09071",
  "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",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7212025568",
  "pdf_url": "https://arxiv.org/pdf/2609.09071",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2dtb2hchggmpq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:52Z",
      "native_id": "2609.09071",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09071"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "The Path Integral Monte Carlo Sign Problem Is Not Always NP-Hard: Harmonic Fermions Can Be Solved in Quadratic Time",
  "title_text": "The Path Integral Monte Carlo Sign Problem Is Not Always NP-Hard: Harmonic Fermions Can Be Solved in Quadratic Time",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:52Z",
  "url": "https://research.draconitic.com/paper/2dtb2hchggmpq",
  "venue": "arXiv",
  "versions": []
}