Low-temperature hopping dynamics with energy disorder: Renormalization group approach

Abstract

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 hierarchical process, 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 degrees of energy disorder, and find the approach to be accurate at low temperatures and computationally much faster than the brute-force 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 pre-exponential factors of the Miller-Abrahams model are analyzed.