Quantum entanglement and fidelity of the two-site Holstein model

We study the polaronic crossover properties in the two-site Holstein model by the quantum entanglement and the fidelity. Based on the exact wave function obtained by the extended bosonic coherent states, the linear entropy and the fidelity are evaluated. The maximum of the entanglement between the electron and surrounding phonons is observed in a small polaron regime. A smooth change (no singularity) of the ground-state fidelity as well as its susceptibility appears in the intermediate coupling regime, which confirms a crossover rather than a phase transition in this system by this quantum information tool. In addition, the results for some quantities in the weak-coupling and strong-coupling limit are given analytically.