{
  "abstract": "Purified Gibbs states provide a bridge between finite-temperature physics, dissipative dynamics, and ground-state methods. In this work, we study the exact finite sum-of-squares (SoS) construction of their parent Hamiltonians and the associated Lindbladian based on modular annihilators. Given a finite set of Hermitian generators, the corresponding modular annihilators yield a frustration-free SoS representation without continuous time integrals or an explicit decomposition into Bohr-frequency sectors. The purified Gibbs state remains a common zero mode while the freedom to choose and combine the generators can be used to optimize the spectral properties of the parent Hamiltonian. For free-fermion Hamiltonians, modular transformations act linearly on Majorana operators, leading to an analytically solvable family of parent Hamiltonians parameterized by a real symmetric coefficient matrix \\(S\\). For the scalar-functional subclass $S=f(h)$, we show that, at fixed operator norm, the choice $S_{\\mathrm{opt}}\\propto 1/\\sqrt{\\cosh(2βh)}$ has mixing time upper bound $2\\log(2N/ε)$ for any $β$, which exhibits rapid mixing and is irrelevant to the inverse temperature $β$. For interacting systems, where the modularly dressed generators are not available in closed form, we introduce a Krylov--Lanczos approximation scheme and bound the resulting ground-state error in terms of the modular-approximation error and the parent-Hamiltonian gap. Numerical results illustrate the free-fermion spectral advantage and show how the accuracy of the interacting construction depends on temperature, interaction strength, and Krylov dimension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30272",
  "author_total": 3,
  "authors": [
    {
      "name": "Changhao Yi"
    },
    {
      "name": "Jun Takahashi"
    },
    {
      "name": "Cunlu Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cysns6qktz8zw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30272",
  "fulltext_url": null,
  "id": "cysns6qktz8zw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30272",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7204865346",
  "pdf_url": "https://arxiv.org/pdf/2608.30272",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cysns6qktz8zw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.30272",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30272"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Modular-Annihilator Parent Hamiltonians for Purified Gibbs States: Spectral Design and Controlled Approximation",
  "title_text": "Modular-Annihilator Parent Hamiltonians for Purified Gibbs States: Spectral Design and Controlled Approximation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/cysns6qktz8zw",
  "venue": "arXiv",
  "versions": []
}