Effects of boson dispersion in fermion-boson coupled systems

We study the nonlinear feedback in a fermion-boson system using an extension of dynamical mean-field theory and the quantum Monte Carlo method. In the perturbative regimes (weak-coupling and atomic limits) the effective interaction among fermions increases as the width of the boson dispersion increases. In the strong-coupling regime away from the antiadiabatic limit, the effective interaction decreases as we increase the width of the boson dispersion. This behavior is closely related to complete softening of the boson field. We elucidate the parameters that control this nonperturbative region where fluctuations of the dispersive bosons enhance the delocalization of fermions.