Metal-insulator transition in one-dimensional quasi-periodic systems

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Abstract
The authors use the vector recursion method of Haydock to obtain the transmittance of a class of generalised Harper model in one dimension and to study the metal-insulator transition in this model. They also study the Argand map of the complex transmission coefficient which contains information about the phase change of the wavefunctions as they travel through the chain. This method of location of the metal-insulator transition is computationally easy and fast and does not require cumbersome formulae for calculating the localization length involving diagonalization of very large matrices, and assumptions of exponential localization. Moreover, the authors may use their methodology to analyse situations where they have non-exponential localization.