Schwinger-Keldysh field theory for operator R\'{e}nyi entropy and entanglement growth in non-interacting systems with sub-ballistic transports
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Quantum Physics arXiv:2602.22331 (quant-ph) [Submitted on 25 Feb 2026] Title:Schwinger-Keldysh field theory for operator Rényi entropy and entanglement growth in non-interacting systems with sub-ballistic transports Authors:Priesh Roy, Sumilan Banerjee View a PDF of the paper titled Schwinger-Keldysh field theory for operator R\'{e}nyi entropy and entanglement growth in non-interacting systems with sub-ballistic transports, by Priesh Roy and 1 other authors View PDF HTML (experimental) Abstract:The notion of operator growth in quantum systems furnishes a bridge between transport and the generation of entanglement between different parts of the system under quantum dynamics. We define a measure of operator growth in terms of subsystem operator Rényi entropy, which provides a state-independent measure of operator growth, unlike entanglement entropies, and the usual measures of operator growth like out-of-time-order correlators. We show that the subsystem operator Rényi entropy encodes both spatial and temporal information, and thus can directly connect to transport for a local operator related to a conserved quantity. We construct a unified Schwinger-Keldysh (SK) field theory formalism for the time evolution of operator Rényi entropy and entanglement entropies of initial pure states. We use the SK field theory to obtain the operator Rényi and state entanglement entropies in terms of infinite-temperature and vacuum Keldysh Green's functions, respectively, for non-interacting systems. We apply the method to explore the connection between operator and entanglement growth, and transport in non-interacting systems with quasiperiodic and random disorder, like the one- and two-dimensional Aubry-André models and the two-dimensional Anderson model. In particular, we show that the growth of subsystem operator Rényi entropy and state von Neumann and Rényi entanglement entropies can capture both ballistic and sub-ballistic transport behaviors, like diffusive and anomalous diffusive transport, as well as localization in these systems. Comments: Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); High Energy Physics - Theory (hep-th) Cite as: arXiv:2602.22331 [quant-ph] (or arXiv:2602.22331v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.22331 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Priesh Roy [view email] [v1] Wed, 25 Feb 2026 19:00:28 UTC (4,472 KB) Full-text links: Access Paper: View a PDF of the paper titled Schwinger-Keldysh field theory for operator R\'{e}nyi entropy and entanglement growth in non-interacting systems with sub-ballistic transports, by Priesh Roy and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: cond-mat cond-mat.dis-nn hep-th 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)