  We study the interplay between strong electron-electron and electron-phonon
interactions within a two-orbital molecule coupled to metallic leads, taking
into account Holstein-like coupling of a local phonon mode to the molecular
charge as well as phonon-mediated interorbital tunneling. By combining
canonical transformations with numerical renormalization-group calculations to
address the interactions nonperturbatively and on equal footing, we obtain a
comprehensive description of the system's many-body physics in the
anti-adiabatic regime where the phonons adjust rapidly to changes in the
orbital occupancies, and are thereby able to strongly affect the Kondo physics.
The electron-phonon interactions strongly modify the bare orbital energies and
the Coulomb repulsion between electrons in the molecule, and tend to inhibit
tunneling of electrons between the molecule and the leads. The consequences of
these effects are considerably more pronounced when both molecular orbitals lie
near the Fermi energy of the leads than when only one orbital is active. In
situations where a local moment forms on the molecule, there is a crossover
with increasing electron-phonon coupling from a regime of collective Kondo
screening of the moment to a limit of local phonon quenching. At low
temperatures, this crossover is associated with a rapid increase in the
electronic occupancy of the molecule as well as a marked drop in the linear
electrical conductance through the single-molecule junction.
