{
  "abstract": "We first show that, for the SU(N) Heisenberg model with isotropic two-site interactions on an arbitrary lattice of Ns sites, the full spectrum in its singlet sector (when N divides Ns) is the negative of the full spectrum in its singlet sector of the SU(Ns/N) Heisenberg model defined on the same lattice. This theorem, valid for models with the fundamental irreducible representation (irrep) at each lattice site, follows naturally from a transposition operation in the basis of Standard Young Tableaux (SYTs). Second, this basis -- previously recognized as particularly convenient for exact diagonalization (ED) of SU(N) Heisenberg models -- admits an efficient, memory-saving implementation, thereby enabling large-scale diagonalizations for unprecedented system sizes Ns and numbers of colors N>3. We apply these ideas to an ED study of the SU(4) and SU(7) Heisenberg models on the triangular lattice (TL), extending the calculations up to Ns=28 sites. In particular, starting from the SU(4) case, whose nearest-neighbor ground state remains debated, we confirm that next-nearest-neighbor couplings stabilize four-sublattice long-range order. We further find that increasing the number of colors from N=4 to N=7 provides another route toward a Néel-like ground state, even without such additional couplings. N = 4 to N = 7 provides another route toward a Néel-like ground state, even without such additional couplings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15162",
  "author_total": 2,
  "authors": [
    {
      "name": "Samuel Gozel"
    },
    {
      "name": "Pierre Nataf"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d3cqkedby7fpw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15162",
  "fulltext_url": null,
  "id": "d3cqkedby7fpw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15162",
  "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",
      "cond-mat.str-el"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7221805341",
  "pdf_url": "https://arxiv.org/pdf/2610.15162",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d3cqkedby7fpw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.15162",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15162"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Spectral Mapping Theorem between SU(N) and SU(Ns/N) Heisenberg Models and Exact Diagonalization of SU(4) and SU(7) Long-Range Ordered Phases on the Triangular Lattice",
  "title_text": "Spectral Mapping Theorem between SU(N) and SU(Ns/N) Heisenberg Models and Exact Diagonalization of SU(4) and SU(7) Long-Range Ordered Phases on the Triangular Lattice",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:06Z",
  "url": "https://research.draconitic.com/paper/d3cqkedby7fpw",
  "venue": "arXiv",
  "versions": []
}