Polaronic and nonadiabatic phase diagram from anomalous isotope effects

Isotope effects (IEs) are powerful tools to probe directly the dependence of many physical properties on lattice dynamics. In this Letter we investigate the onset of anomalous IEs in the spinless Holstein model by employing the dynamical mean field theory. We show that the isotope coefficients of the electron effective mass and of the dressed phonon frequency are sizable also far away from the polaronic crossover and mark the importance of nonadiabatic lattice fluctuations. We draw a nonadiabatic phase diagram in which we identify a novel crossover, not related to polaronic features, where the IEs attain their largest anomalies.