  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.
