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

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 charging energy and exchange coupling terms. Although this formalism typically decouples the charge and spin components, confinement-induced energy splitting can induce unexpected entanglement within the system. By analyzing the dynamic susceptibility and quantum Fisher information (QFI), significant behaviors are uncovered influenced by exchange constants, temperature variations, and confinement effects. In QDs with Ising exchange interactions, far below the Stoner instability (SI) point, where the QD is in a disordered paramagnetic phase, temperature reductions lead to decreased entanglement, challenging conventional expectations. These findings demonstrate that for QDs with small exchange interactions, the responses of easy-plane ($J_z<J_{\perp }$) and easy-axis ($J_z>J_{\perp }$) configurations are similar, with increased anisotropy broadening susceptibility and shifting its maximum to higher frequencies. For large exchange interactions, the susceptibility differences between easy-plane and easy-axis QDs become significant, with easy-plane QDs exhibiting a higher susceptibility magnitude. Additionally, the study reveals that temperature variations affect the dynamic response functions differently in easy-axis and easy-plane QDs. In easy-plane QDs, QFI consistently decreases with increasing temperature, whereas in easy-axis QDs, QFI behavior is highly dependent on the strengths of $J_z$ and $J_{\perp }$, showing either an increase or decrease with temperature based on specific coupling conditions. Conversely, at low temperatures, anisotropic Heisenberg models exhibit enhanced entanglement near isotropic points. Overall, this work contributes to advancing the understanding of entanglement in QDs and its potential applications in quantum technologies.