Isotope effects in the Hubbard-Holstein model within dynamical mean-field theory

We study the isotope effects arising from the coupling of correlated electrons with dispersionless phonons by considering the Hubbard-Holstein model at half-filling within the dynamical mean-field theory. In particular we calculate the isotope effects on the quasiparticle spectral weight Z, the renormalized phonon frequency, and the static charge and spin susceptibilities. In the weakly correlated regime U/t less than or similar to 1.5, where U is the Hubbard repulsion and t is the bare electron half-bandwidth, the physical properties are qualitatively similar to those characterizing the Holstein model in the absence of Coulomb repulsion, where the bipolaronic binding takes place at large electron-phonon coupling and it is reflected in divergent isotope responses. On the contrary in the strongly correlated regime U/t greater than or similar to 1.5, where the bipolaronic metal-insulator transition becomes of first order, the isotope effects are bounded, suggesting that the first-order transition is likely driven by an electronic mechanism, rather then by a lattice instability. These results point out how the isotope responses are extremely sensitive to phase boundaries and they may be used to characterize the competition between the electron-phonon coupling and the Hubbard repulsion.