Abstract
A new decimation scheme is introduced to study localization transitions in tight binding models with long range interaction. Within this scheme, the lattice models are mapped to a vectorized dimer where an asymptotic dissociation of the dimer is shown to correspond to the vanishing of the transmission coefficient through the system. When applied to the kicked Harper model, the method unveils an intricately nested extended and localized phases in two-dimensional parameter space. In addition to computing transport characteristics with extremely high precision, the renormalization tools also provide a new method to compute quasienergy spectrum.
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