Polaronic quantum diffusion in dynamic localization regime

We investigate the quantum dynamics in a disordered electronic lattice with Fibonacci sequence of site energy and off-diagonal electron-phonon coupling within a sub-Ohmic bath by the time-dependent density matrix renormalization group algorithm. It is found that, the slope of the inverse participation ratio versus the coupling strength undergoes a sudden change indicating a transition from the static to the dynamic localization. In the dynamic localization regime, the generated polarons coherently diffuse via hopping-like processes evidenced by the saturated entanglement entropy, providing a novel scenario for the transportation mechanism in strongly disordered systems. The mean-square displacement is revealed to be insensitive to the coupling strength, implying the quantum diffusion behavior survives the energy disorder that prevails in real organic materials.