{
  "abstract": "We formulate the matrix product state (MPS) tangent-space excitation construction for finite, non-uniform systems with open boundary conditions, using the smooth full-rank stratum of the MPS variety as the variational manifold. The resulting linear tangent ansatz yields a projected-Hamiltonian eigenproblem for approximating excitation spectra. We further introduce a rank tomography that characterizes the particle-sector expressivity of the MPS tangent space. For number-conserving systems, we resolve the Schmidt ranks of reference states by particle number and derive an explicit relation between the resulting rank profile and the dimensions of the tangent-space sectors. This allows sector completeness and parametric deficiency to be determined directly from the reference state, without explicitly constructing a tangent basis, and provides a direct diagnostic of the sectorwise expressivity of the MPS excitation ansatz. We benchmark the finite-system construction on Bose--Hubbard chains against exact diagonalization, finding accurate low-lying excitation branches while identifying sector-dependent limitations of the linear tangent ansatz.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.05269",
  "author_total": 2,
  "authors": [
    {
      "name": "Otto T. P. Schmidt"
    },
    {
      "name": "Iacopo Carusotto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/44v33ze66wzc5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.05269",
  "fulltext_url": null,
  "id": "44v33ze66wzc5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.05269",
  "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.quant-gas"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7167599431",
  "pdf_url": "https://arxiv.org/pdf/2607.05269",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/44v33ze66wzc5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2607.05269",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.05269"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.quant-gas",
      "subfield": "amo"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.quant-gas",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Excitation spectra and rank tomography of finite MPS tangent spaces",
  "title_text": "Excitation spectra and rank tomography of finite MPS tangent spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:37Z",
  "url": "https://research.draconitic.com/paper/44v33ze66wzc5",
  "venue": "arXiv",
  "versions": []
}