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Low-Temperature Hopping Dynamics with Energy Disorder: Renormalization Group Approach

We formulate a real-space renormalization group (RG) approach for efficient numerical analysis of the low-temperature hopping dynamics in energy-disordered lattices. The approach explicitly relies on the time-scale separation of the trapping/escape dynamics. This time-scale separation allows to treat the hopping dynamics as a hierarchal process, an RG step being a transformation between the levels of the hierarchy. We apply the proposed RG approach to analyze hopping dynamics in one- and two-dimensional lattices with varying degree of energy disorder, and find the approach to be more accurate at low temperatures and computationally much faster, than the direct diagonalization. Applicability criteria of the proposed approach with respect to the time-scale separation and the maximum number of hierarchy levels are formulated. RG flows of energy distribution and preexponents of the Miller-Abrahams model are analyzed.