Polaron crossover and bipolaronic metal-insulator transition in the half-filled Holstein model

The formation of a finite density multipolaronic state in the Holstein model is analyzed by means of the Dynamical mean-field theory at zero and finite temperature. The spinless and spinful fermion cases are compared to disentangle the polaron crossover from the bipolaron formation. We show that polaron formation is not associated to a metal-insulator transition, which is instead due to bipolaron formation. In the spinful case a region of bound pairs without significant lattice distortion appears between the weak-coupling regime and the strong-coupling bipolaronic phase. This region shrinks with increasing temperature and with decreasing phonon frequency.