{
  "abstract": "We introduce $Krylov$ $edge$ $spectroscopy$, a many-body operator-space protocol for detecting and classifying one-dimensional symmetry-protected topological phases from local boundary dynamics. A Hermitian boundary operator generates a semi-infinite Krylov hopping chain whose boundary weight obeys an exact zero-frequency normalizability criterion. Open-periodic, boundary-bulk, and symmetry-preserving boundary-perturbation tests identify protected boundary memory, while a finite-depth leakage residual certifies when an explicitly reconstructed operator is already near zero frequency. Classification minimizes the normalized commutator over symmetry-resolved boundary operators in fixed charge sectors. For bosonic $\\mathbb{Z}_N \\times \\mathbb{Z}_N$ phases, the recovered endpoint charge gives the cohomology label. The method requires no explicit ground-state wavefunction, entanglement spectrum, or guessed dressed edge or string operator. For finite-range Hamiltonians, locality eliminates full-system exact diagonalization and guarantees thermodynamic-limit convergence at fixed Krylov depth. We demonstrate the protocol in cluster, clock, Haldane, and trivial spin-1 chains. In the exactly solvable cluster chain, the transition between the gapped topological and trivial phases manifests as a localization-delocalization transition of the Krylov edge mode on the Krylov chain. This transition occurs precisely at the bulk gap closing, and its localization-length exponent coincides with the Ising correlation-length exponent. Through operator Krylov dynamics, our work turns local boundary evolution into a direct spectroscopy of many-body topology.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10676",
  "author_total": 2,
  "authors": [
    {
      "name": "Heiko Georg Menzler"
    },
    {
      "name": "Rishabh Jha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3n9nqy3394p0g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10676",
  "fulltext_url": null,
  "id": "3n9nqy3394p0g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10676",
  "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",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Topological Materials and Phenomena"
    ]
  ],
  "openalex": "W7212309003",
  "pdf_url": "https://arxiv.org/pdf/2609.10676",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3n9nqy3394p0g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.10676",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10676"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Krylov Edge Spectroscopy of Symmetry-Protected Topological Phases",
  "title_text": "Krylov Edge Spectroscopy of Symmetry-Protected Topological Phases",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:19Z",
  "url": "https://research.draconitic.com/paper/3n9nqy3394p0g",
  "venue": "arXiv",
  "versions": []
}