Title: Entanglement in Quantum Dots: Insights from Dynamic Susceptibility and Quantum Fisher Information

Abstract: This study investigates the entanglement properties of quantum dots (QDs) under a universal Hamiltonian where the Coulomb interaction between particles (electrons or holes) decouples into a charging energy and an exchange coupling term. While this formalism typically decouples the charge and spin components, the confinement-induced energy splitting can induce unexpected entanglement in the system. By analyzing the dynamic susceptibility and quantum Fisher information (QFI), we uncover intriguing behaviors influenced by exchange constants, temperature variations, and confinement effects. In Ising QDs, far below the Stoner instability point where the QD is in a disordered paramagnetic phase, temperature reductions unexpectedly lead to decreased entanglement, challenging conventional expectations. Conversely, anisotropic Heisenberg models exhibit enhanced entanglement near isotropic points. Our findings highlight the intricate interplay between exchange interactions and entanglement in QDs, laying the groundwork for future studies on topological entanglement and the influence of entanglement on material properties. Overall, this work contributes to advancing our understanding of entanglement in QDs and its potential applications in quantum technologies.