{
  "abstract": "Over the past decade, high-order series expansions based on linked-cluster methods have become an important tool for studying low-energy properties of gapped quantum systems with long-range interactions. We introduce a deterministic framework that removes a central computational bottleneck of this method. Our graph zeta method replaces the costly and statistically noisy Monte Carlo (MC) evaluation of high-dimensional lattice sums by a systematic, high-precision computation that delivers series coefficients within minutes on standard desktop hardware. The full momentum-dependent series is obtained in a single calculation, enabling high-resolution excitation spectra throughout the Brillouin zone. Building on the companion paper [1], the method reformulates graph-embedding sums as graph zeta functions and decomposes them into blocks classified by their treewidth tw. Low-treewidth blocks (tw$\\leq2$) admit closed expressions based on Epstein zeta functions, while higher-treewidth blocks (tw$>2$) are evaluated using tensor-network bucket elimination. We benchmark the approach for transverse-field Ising models with power-law interactions in 1d, 2d, and 3d, reproducing previous MC results at a fraction of the computational cost while enabling substantially denser parameter sampling. An open-source implementation makes the method directly applicable to general interactions and large parameter scans. As an application, we compare microscopic interaction models for the stacked quasi-2d transverse-field Ising triangular-lattice antiferromagnet KTmSe$_2$ and find that a model including dipolar interactions best describes existing experimental data. The graph zeta method thus turns high-order linked-cluster expansions into a practical and deterministic tool for fast quantitative momentum-resolved modeling of short- and long-range quantum matter.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18761",
  "author_total": 5,
  "authors": [
    {
      "name": "Antonia Duft"
    },
    {
      "name": "Patrick Adelhardt"
    },
    {
      "name": "Jan Alexander Koziol"
    },
    {
      "name": "Andreas A. Buchheit"
    },
    {
      "name": "Kai Phillip Schmidt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ynbs7ej0v1kv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18761",
  "fulltext_url": null,
  "id": "3ynbs7ej0v1kv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18761",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7213511268",
  "pdf_url": "https://arxiv.org/pdf/2609.18761",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ynbs7ej0v1kv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2609.18761",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18761"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Exact and fast series expansions for quantum models with long-range interactions",
  "title_text": "Exact and fast series expansions for quantum models with long-range interactions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/3ynbs7ej0v1kv",
  "venue": "arXiv",
  "versions": []
}