{
  "abstract": "The monomer-dimer model is one of the most well-known unsolved lattice models. In this paper we study the monomer-dimer model on the honeycomb lattice using the tensor network method, in the case that the dimer and monomer activities are 1. The monomer-dimer configurations are exactly mapped into the ground states of the antiferromagnetic Ising model on the Kagomé lattice in the critical field $H_{\\rm{ex}}=4J$, and the tensor network is constructed based on the local ground states of each Ising triangle. The VUMPS approach is employed to contract the tensor network, providing a high-precision result of the monomer-dimer problem. We also revisit the edge coloring problem on the honeycomb lattice and discuss its relationship to the monomer-dimer model. Finally we formulate the monomer-dimer problem in the language of the sixteen-vertex model, and discuss the non-integrability of the general monomer-dimer model and the integrability of the pure dimer model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07899",
  "author_total": 3,
  "authors": [
    {
      "name": "De-Zhang Li"
    },
    {
      "name": "Jie Liu"
    },
    {
      "name": "Xin Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f9a0z7367a3zn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07899",
  "fulltext_url": null,
  "id": "f9a0z7367a3zn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07899",
  "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.mes-hall"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7212009494",
  "pdf_url": "https://arxiv.org/pdf/2609.07899",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f9a0z7367a3zn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.07899",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07899"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Tensor network investigation of the monomer-dimer model on the honeycomb lattice",
  "title_text": "Tensor network investigation of the monomer-dimer model on the honeycomb lattice",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:48Z",
  "url": "https://research.draconitic.com/paper/f9a0z7367a3zn",
  "venue": "arXiv",
  "versions": []
}