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Predicting entanglement entropy from particle tunneling of interacting fermions using Kolmogorov-Arnold networks

Elvira Bilokon1,2,*, Valeriia Bilokon1,2,†, Abhijit Sen1,‡, Mohammed Th. Hassan3,4,§, Andrii G. Sotnikov2,5,∥, and Denys I. Bondar1,¶

  • *Contact author: ebilokon@tulane.edu
  • †Contact author: vbilokon@tulane.edu
  • ‡Contact author: abhijit913@gmail.com
  • §Contact author: mohammedhassan@arizona.edu
  • ∥Contact author: a_sotnikov@kipt.kharkov.ua
  • Contact author: dbondar@tulane.edu
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Phys. Rev. Research 8, 033243 – Published 28 August, 2026

DOI: https://doi.org/10.1103/1tb7-dmtf

Abstract

Entanglement entropy is a fundamental measure of quantum correlations and a key resource underpinning advances in quantum information and many-body physics. We uncover a universal relationship between bipartite entanglement entropy and particle number after the barrier in a one-dimensional Fermi-Hubbard system with an external asymmetric potential. Decomposing the von Neumann entropy into number entropy Sn and configurational entropy Sc, we show that in the barrier-dominated tunneling regime both components are individually well-defined functions of the postbarrier particle density nA, even though Sc encodes off-diagonal coherences that are not directly accessible from density measurements alone. Using Kolmogorov-Arnold networks—a novel machine learning architecture—we learn the relationship for entropy and its components across a broad range of interaction strengths and barrier heights with high predictive accuracy. Furthermore, we propose a simple analytical binary-entropy-like expression that quantitatively captures the observed correlation for fixed parameters. Our findings open avenues for characterizing quantum correlations in transport phenomena and provide a powerful framework for estimating the full von Neumann entropy—including its configurational component—from a single transport observable.

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Outline

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Phys. Rev. Research 8, 033243– Published 28 August, 2026
  • Received 15 August 2025
  • Revised 12 June 2026
  • Accepted 10 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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