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Anomalously large critical regions in power-law random matrix ensembles

E. Cuevas·V. Gasparian·M. Ortuno
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Abstract

We investigate numerically the power-law random matrix ensembles. Wavefunctions are fractal up to a characteristic length whose logarithm diverges asymmetrically with different exponents, 1 in the localized phase and 0.5 in the extended phase. The characteristic length is so anomalously large that for macroscopic samples there exists a finite critical region, in which this length is larger than the system size. The Green's functions decrease with distance as a power law with an exponent related to the correlation dimension.

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E. Cuevas, V. Gasparian, M. Ortuno. 2001-06-22. Anomalously large critical regions in power-law random matrix ensembles. https://doi.org/10.1103/physrevlett.87.056601

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