Quasi-particle dynamics of a strongly correlated polaron metal

We develop a simple diagrammatic low-energy boson exchange strong-coupling model for an antiferromagnetically correlated polaronic metal. Important low-temperature features of such a model are (i) a large polaronic mass enhancement $Z$ and a strongly narrowed, low-energy, near-Fermi-level van Hove resonance peak in the interacting density of states at temperatures $T$ well below the lattice tunneling energy scale $\Omega_t$; (ii) a rapid thermal suppression of $Z$ and of the van Hove resonance which occurs when the temperature $T$ becomes comparable to the lattice tunneling excitation energy scale $\Omega_t$; and (iii) strong isotopic mass dependence of the electronic mass enhancement $Z$ at temperatures $T$ well below $\Omega_t$. Surprisingly, in spite of the large low-$T$ mass enhancment, the anharmonic lattice fluctuations in the high temperature regime $T\gsim\Omega_t$, give rise only to a moderate, essentially $T$-independent quasi-particle damping. We suggest possible low temperature isotope experiments to explore polaronic fluctuations in the cuprates superconductors.