Level number variance and spectral compressibility in a critical two-dimensional random matrix model

A. Ossipov; I. Rushkin; E. Cuevas

doi:10.1103/physreve.85.021127

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arXiv · 1111.3520

Level number variance and spectral compressibility in a critical two-dimensional random matrix model

A. Ossipov·I. Rushkin·E. Cuevas

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Abstract

We study level number variance in a two-dimensional random matrix model characterized by a power-law decay of the matrix elements. The amplitude of the decay is controlled by the parameter b. We find analytically that at small values of b the level number variance behaves linearly, with the compressibility chi between 0 and 1, which is typical for critical systems. For large values of b, we derive that chi=0, as one would normally expect in the metallic phase. Using numerical simulations we determine the critical value of b at which the transition between these two phases occurs.

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A. Ossipov, I. Rushkin, E. Cuevas. 2011-11-15. Level number variance and spectral compressibility in a critical two-dimensional random matrix model. https://doi.org/10.1103/physreve.85.021127

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