Bipolarons and polarons in the Holstein-Hubbard model: Analogies and differences

The single bipolaron problem is examined in the context of the 1D Holstein-Hubbard model, emphasizing analogies and differences with respect to the complementary single polaron physics. The bipolaron band structure below the phonon threshold is revealed, showing a complex relationship between numerous excited bands as the adiabatic limit is approached. Light bipolarons with significant binding energy, the stability of large bipolarons, the small to large bipolaron crossover as a function of the Hubbard repulsion, as well as the bipolaron dissociation, are investigated in detail, disentangling adiabatic, nonadiabatic and lattice coarsening effects. It is emphasized that condensation of bipolarons occurs in the dilute limit only at very low temperatures.