{
  "abstract": "This thesis develops diagrammatic methods for thermodynamic and subsystem quantities of interacting lattice fermions, providing reference calculations for quantum simulators and many-body approximations. I formulate an inverse-flavour expansion about a self-consistent Hartree saddle, enumerate non-Gaussian diagrams, and use a discrete Lehmann representation to integrate selected internal vertices analytically. Density results cover 31 state points of the six-flavour Hubbard model on a $70\\times70$ lattice at $T/t=0.15$. I generalize combinatorial summation to flavour-dependent propagators and expansion shifts. CoS++ combines partial contractions to obtain connected sums for interaction subsets. A determinant-polynomial sieve evaluates the same sums through local coefficient filters; at ninth order it is 24--25 times faster than the specified CoS baselines in three-flavour dense-random-matrix benchmarks. Thermodynamic applications include a 2048-site honeycomb lattice and a three-flavour square lattice with 1024 sites. For the second Renyi entropy, I derive a fermionic replica path integral and a stable evaluation of its two-time Green functions. The connected-determinant calculation reaches tenth order on a $3\\times3$ cluster and ninth order on larger lattices. On $50\\times50$ sites at $(U/t,μ/t,βt)=(3,1,8)$, the ninth-order continuation at shift $α=1.3$ gives $S_2/N_s=0.06695$ with propagated Monte Carlo uncertainty $3.0\\times10^{-5}$. Comparing two expansion shifts at their respective retained orders gives an endpoint difference of $2.6\\times10^{-4}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37505",
  "author_total": 1,
  "authors": [
    {
      "name": "Boyuan Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f13b6j49xm0g3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37505",
  "fulltext_url": null,
  "id": "f13b6j49xm0g3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37505",
  "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.str-el"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7224135617",
  "pdf_url": "https://arxiv.org/pdf/2610.37505",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f13b6j49xm0g3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.37505",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37505"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    }
  ],
  "title": "New Developments in Diagrammatic Monte Carlo for Interacting Lattice Fermions: Efficient Algorithms and Applications",
  "title_text": "New Developments in Diagrammatic Monte Carlo for Interacting Lattice Fermions: Efficient Algorithms and Applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:50Z",
  "url": "https://research.draconitic.com/paper/f13b6j49xm0g3",
  "venue": "arXiv",
  "versions": []
}