{
  "abstract": "We prove rapid mixing of a quantum Gibbs sampler for general one-dimensional non-commuting local spin systems at every fixed positive temperature. In particular, for a system of $n$ sites, we show that the Kubo--Martin--Schwinger (KMS) detailed-balanced Gibbs sampler of~\\cite{CKG2023} converges from any initial state to trace-norm error $ε$ in time $O(\\log^4(n)+\\log(1/ε))$. This improves the previous $O(n+\\log(1/ε))$ bound and establishes rapid mixing beyond high-temperature and weak-interaction regimes. Our proof explains why the slowest decay rate, captured by the spectral gap, can substantially underestimate the speed of equilibration. The key insight is that a state far from equilibrium must have a substantial component outside the span of low-weight Pauli operators, where stronger dissipation estimates apply. This yields two stages of relaxation: a double-exponential convergence from a bad initial state, followed by exponential convergence near equilibrium. We turn this mechanism into a framework for proving rapid mixing through spectral analysis beyond the gap. Our decay estimate is equivalent to exponential convergence in sandwiched Rényi-2 divergence. Together with the spectral gap, it also implies a modified logarithmic Sobolev inequality with rate $Ω(\\log^{-4}(n))$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05848",
  "author_total": 2,
  "authors": [
    {
      "name": "Hongrui Chen"
    },
    {
      "name": "Zhiyan Ding"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/77dch1bwejhn6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05848",
  "fulltext_url": null,
  "id": "77dch1bwejhn6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05848",
  "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"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220869575",
  "pdf_url": "https://arxiv.org/pdf/2610.05848",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/77dch1bwejhn6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:18Z",
      "native_id": "2610.05848",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05848"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Spectral Analysis Beyond the Spectral Gap: Rapid Mixing of Quantum Gibbs Samplers in One Dimension",
  "title_text": "Spectral Analysis Beyond the Spectral Gap: Rapid Mixing of Quantum Gibbs Samplers in One Dimension",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/77dch1bwejhn6",
  "venue": "arXiv",
  "versions": []
}