Process-tensor approach to full counting statistics of charge transport in quantum many-body circuits
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Quantum Physics arXiv:2603.28894 (quant-ph) [Submitted on 30 Mar 2026] Title:Process-tensor approach to full counting statistics of charge transport in quantum many-body circuits Authors:Hari Kumar Yadalam, Mark T. Mitchison View a PDF of the paper titled Process-tensor approach to full counting statistics of charge transport in quantum many-body circuits, by Hari Kumar Yadalam and 1 other authors View PDF Abstract:We introduce a numerical tensor-network method to compute the statistics of the charge transferred across an interface partitioning an interacting one-dimensional many-body lattice system with $U(1)$ symmetry. Our approach is based on a matrix-product state representation of the process tensor (also known as influence functional or influence matrix) describing the effect of the bulk system on the degrees of freedom at the interface, allowing us to evaluate a multi-time correlation function that yields the moment-generating function of charge transfer. We develop a scheme to truncate non-Markovian correlations which preserves the proper normalization of the process tensor and ensures the correct physical properties of the generating function. We benchmark our approach by simulating magnetization transport within the Heisenberg spin-$1/2$ XXZ brickwork circuit model at infinite temperature. Our results recover the correct transport exponent describing ballistic, superdiffusive, and diffusive transport in different regimes of the model. We also demonstrate anomalous transport encoded by a self-similar scaling form of the moment-generating function outside of the ballistic regime. In particular, we confirm the breakdown of Kardar-Parisi-Zhang universality in higher-order transport cumulants at the isotropic point. Our work paves the way for process-tensor descriptions of non-Markovian open quantum systems to address current fluctuations in strongly interacting systems far from equilibrium. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Computational Physics (physics.comp-ph) Cite as: arXiv:2603.28894 [quant-ph] (or arXiv:2603.28894v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.28894 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Hari Kumar Yadalam [view email] [v1] Mon, 30 Mar 2026 18:17:19 UTC (2,760 KB) Full-text links: Access Paper: View a PDF of the paper titled Process-tensor approach to full counting statistics of charge transport in quantum many-body circuits, by Hari Kumar Yadalam and 1 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: cond-mat cond-mat.stat-mech cond-mat.str-el physics physics.comp-ph 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?)