Kondo effect and the fate of bistability in molecular quantum dots with strong electron-phonon coupling

We investigate the properties of the molecular quantum dot (Holstein-Anderson) model using numerical and analytical techniques. Path integral Monte Carlo simulations for the cumulants of the distribution function of the phonon coordinate reveal that at intermediate temperatures the effective potential for the oscillator exhibits two minima rather than a single one, which can be understood as a signature of a bistability effect. A straightforward adiabatic approximation turns out to adequately describe the properties of the system in this regime. Upon lowering the temperature the two potential energy minima of the oscillator merge to a single one at the equilibrium position of the uncoupled system. Using the parallels to the X-ray edge problem in metals we derive the oscillator partition function. It turns out to be identical to that of the Kondo model, which is known to possess a universal low energy fixed point characterized by a single parameter -- the Kondo temperature $T_K$. We derive an analog of $T_K$ for the molecular quantum dot model, present numerical evidence pointing towards the appearance of the Kondo physics and discuss experimental implications of the discovered phenomena.