{
  "abstract": "We give a finite-temperature test for the stability of low-energy spectral subspaces. The test uses a local determinant defect for the alpha-z Renyi kernel of two Gibbs states and bounds the tracial L2 distance between their low-energy projections. The main tool is a spectral-flattening principle for bounded positive injective operators in a semifinite von Neumann algebra. It reduces the local product defect to an exact two-projection formula. The thermal result applies to lower-bounded affiliated Hamiltonians with trace-class Gibbs operators and does not require the Hamiltonians to be close in operator norm. We give an infinite-level example with unbounded Hamiltonians. For matrices, the result gives a sum of principal-angle remainders. For qubits, the defect and the thermal gaps determine the ground-state overlap exactly. The same estimate gives a uniform error bound for bounded observables in an effective low-energy model. We also prove the determinant inequalities, their equality cases, and z-monotonicity in matrix, finite, and semifinite settings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32095",
  "author_total": 1,
  "authors": [
    {
      "name": "Seyed Mahmoud Manjegani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cncj6h56c5evx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32095",
  "fulltext_url": null,
  "id": "cncj6h56c5evx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32095",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7214701601",
  "pdf_url": "https://arxiv.org/pdf/2609.32095",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cncj6h56c5evx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.32095",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32095"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Local Determinant Defects and Low-Energy Subspace Stability in Semifinite von Neumann Algebras",
  "title_text": "Local Determinant Defects and Low-Energy Subspace Stability in Semifinite von Neumann Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/cncj6h56c5evx",
  "venue": "arXiv",
  "versions": []
}