  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 anti-adiabatic limit,
the effective interaction decreases as we increase the width of the boson
dispersion. This behavior is closely related with 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.
