The effect of dispersive optical phonons on the behaviour of a Holstein polaron

We use the approximation-free Bold Diagrammatic Monte Carlo technique to study the effects of a finite dispersion of the optical phonon mode on the properties of the Holstein polaron, especially its effective mass. For weak electron-phonon coupling the effect is very small, but it becomes significant for moderate and large electron-phonon coupling. The effective mass is found to increase (decrease) if the phonon dispersion has a negative (positive) curvature at the centre of the Brillouin zone.