Entanglement Entropy for Screened Interactions via Dimensional Mapping to Harmonic Oscillators

Quantum Physics arXiv:2601.02877 (quant-ph) [Submitted on 6 Jan 2026] Title:Entanglement Entropy for Screened Interactions via Dimensional Mapping to Harmonic Oscillators Authors:Akshay Kulkarni, Rahul Nigam View a PDF of the paper titled Entanglement Entropy for Screened Interactions via Dimensional Mapping to Harmonic Oscillators, by Akshay Kulkarni and Rahul Nigam View PDF HTML (experimental) Abstract:We investigate interaction-induced corrections to entanglement entropy by mapping a screened Yukawa-type interaction to an effective harmonic oscillator system with controlled anharmonic perturbations. Starting from a one-dimensional interaction $V(x) = -g^2 e^{-\alpha m x}/x$, we reformulate the problem in terms of a four-dimensional radial oscillator, where the finite screening length generates a systematic hierarchy of polynomial interactions in the radial coordinate. This mapping enables a controlled Rayleigh-Schrodinger perturbative treatment of the ground-state wavefunction and an explicit spectral analysis of the reduced density matrix. Working in the weak-screening regime, we compute the leading non-Gaussian correction arising from the quartic interaction $\rho^4$, which appears at order $\alpha^2$ in the expansion of the Yukawa-like potential. We obtain closed analytic expressions for the resulting small eigenvalues of the reduced density matrix and evaluate their contribution to the von Neumann entanglement entropy. We show that the entropy receives analytic corrections at order $\alpha^2$, originating both from explicit anharmonic state-mixing effects and from the implicit $\alpha$ dependence of the Gaussian width parameter. Our results clarify the distinct roles of harmonic renormalization and genuinely non-Gaussian interactions in generating entanglement, establish a systematic power-counting and normalization scheme for higher-order $\rho^{2n}$ perturbations, and provide a transparent oscillator-based framework for computing entanglement entropy in weakly interacting low-dimensional and field-theoretic systems. Comments: Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th) Cite as: arXiv:2601.02877 [quant-ph] (or arXiv:2601.02877v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.02877 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Akshay Kulkarni [view email] [v1] Tue, 6 Jan 2026 10:04:29 UTC (31 KB) Full-text links: Access Paper: View a PDF of the paper titled Entanglement Entropy for Screened Interactions via Dimensional Mapping to Harmonic Oscillators, by Akshay Kulkarni and Rahul NigamView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: 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?)