Title: Exploring Entanglement Spectrum and Phase Diagram in multi-electron Quantum Dot Chains

Abstract: We investigate the entanglement properties in semiconductor quantum dot systems modeled by extended Hubbard model, focusing on the impact of potential energy variations and electron interactions within a four-site quantum dot spin chain. Our study explores local and pairwise entanglement across configurations with electron counts N=4 and N=6, under different potential energy settings. By adjusting the potential energy in specific dots and examining the entanglement across various interaction regimes, we identify significant variations in the ground states of quantum dots. Our results reveal that local potential modifications lead to notable redistributions of electron configurations, significantly affecting the entanglement properties. These changes are depicted in phase diagrams that show entanglement dependencies on interaction strengths and potential energy adjustments, highlighting complex entanglement dynamics and phase transitions triggered by inter-dot interactions.