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Anomalous band center localization in the one-dimensional Anderson model with a disordered distribution of infinite
Yang Cui1, Delong Feng2, Kai Kang3
1CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China and School of Physical Sciences, University of Chinese Academy of Sciences. No. 19A Yuquan Road, Beijing 100049, China.
Abstract:
We perform a detailed numerical study of the influence of distributions without a finite second moment on the Lyapunov exponent through the one-dimensional tight-binding Anderson model with diagonal disorder. Using the transfer matrix parametrization method and considering a specific distribution function, we calculate the Lyapunov exponent numerically and demonstrate its relation with the fractional lower order moments of the disorder probability density function. For the lower order of moments of disorder distribution with an infinite variance, we obtain the anomalous behavior near the band center.
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