  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.
