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

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

2011-11-15

arxiv.org/abs/1111.3520v1

Phys. Rev. E 85, 021127 (2012)

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages

Scientific paper

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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