Two-site Anharmonic Polaronic Model: An Exact Diagonalization Study

Two-site anharmonic polaronic model is considered. The model consists of two sites with local anharmonic phonons and fermions described within the extended two-site Hubbard model. The Hamiltonian matrix is numerically diagonalized in the Hilbert space with all available electronic states and with a finite number of phononic states included so that the lowest energy levels are properly reproduced. In the harmonic case it is found that, depending of the parameter values, the ground state may be either a free polaron state, a bipolaron triplet state, or a bipolaron singlet state. In presence of anharmonicity the crossovers between these states also take place but, due to the induced by anharmonicity renormalization of the electron-phonon coupling αr, the transitions are shifted to higher values of αr