Super-Logarithmic Entanglement Scaling in a Monitored Superconducting Chain

Quantum Physics arXiv:2607.07835 (quant-ph) [Submitted on 8 Jul 2026] Title:Super-Logarithmic Entanglement Scaling in a Monitored Superconducting Chain Authors:Rui-Jing Guo, Zhi-Yuan Wei View a PDF of the paper titled Super-Logarithmic Entanglement Scaling in a Monitored Superconducting Chain, by Rui-Jing Guo and 1 other authors View PDF Abstract:We develop a Keldysh-replica non-linear sigma model (NLSM) for the entanglement dynamics of a monitored one-dimensional spinful $s$-wave BCS chain in the rare-measurement regime, $\gamma \ll J,\Delta$. Although the clean spinful $s$-wave BCS Hamiltonian belongs to symmetry class CI, spin-resolved measurements and projection to a conserved $f$-sector reduce the effective problem to class C. Starting from the corresponding parent symplectic saddle, we show that measurement backaction and the pairing amplitude impose complementary mass constraints that gap out different fluctuation channels. Their interplay dynamically projects the surviving massless modes onto an $\textrm{SO(R)}$ target manifold in replica space. A one-loop renormalization group analysis of this $\textrm{SO(R)}$ NLSM shows that, in the replica limit $R\to1$, the beta function becomes negative, producing a weak-anti-localization flow. This flow yields a super-logarithmic steady-state entanglement scaling $S(L)\sim \ln^2 L$ in the rare-measurement regime. Our field-theoretic result explains the numerical evidence reported in the companion Letter [arXiv:2604.04375] and shows that a topologically trivial monitored $s$-wave superconductor can realize an $\textrm{SO(R)}$ weak-anti-localizing critical phase without relying on a Wess-Zumino-Witten term. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Superconductivity (cond-mat.supr-con) Cite as: arXiv:2607.07835 [quant-ph] (or arXiv:2607.07835v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.07835 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: RuiJing Guo [view email] [v1] Wed, 8 Jul 2026 18:14:30 UTC (53 KB) Full-text links: Access Paper: View a PDF of the paper titled Super-Logarithmic Entanglement Scaling in a Monitored Superconducting Chain, by Rui-Jing Guo and 1 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-07 Change to browse by: cond-mat cond-mat.stat-mech cond-mat.supr-con 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?)