Krylov Edge Spectroscopy of Symmetry-Protected Topological Phases

Quantum Physics arXiv:2609.10676 (quant-ph) [Submitted on 9 Sep 2026] Title:Krylov Edge Spectroscopy of Symmetry-Protected Topological Phases Authors:Heiko Georg Menzler, Rishabh Jha View a PDF of the paper titled Krylov Edge Spectroscopy of Symmetry-Protected Topological Phases, by Heiko Georg Menzler and 1 other authors View PDF 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 neither many-body exact diagonalization, an explicit ground-state wavefunction or entanglement spectrum, nor a guessed dressed edge or string operator. For finite-range Hamiltonians, locality organizes the thermodynamic limit at fixed Krylov depth before the depth limit. 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. Comments: Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2609.10676 [quant-ph] (or arXiv:2609.10676v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.10676 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Rishabh Jha [view email] [v1] Wed, 9 Sep 2026 18:00:01 UTC (137 KB) Full-text links: Access Paper: View a PDF of the paper titled Krylov Edge Spectroscopy of Symmetry-Protected Topological Phases, by Heiko Georg Menzler and 1 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-09 Change to browse by: cond-mat cond-mat.str-el References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)