Predicting Entanglement Entropy from Particle Tunneling of Interacting Fermions Using Kolmogorov-Arnold Networks

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 $S_n$ and configurational entropy $S_c$, we show that in the barrier-dominated tunneling regime both components are individually well-defined functions of the post-barrier particle density $n_A$, even though $S_c$ 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 new 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.

6 pages, 4 figures