Two-dimensional electrons in random magnetic fields: Universality class of random matrices

An analysis is made of the statistics of energy levels for a system of an electron in a square lattice with random magnetic fields. The density of states and the connected density-density correlations are calculated numerically for finite lattice dimension N and energy interval ΔE. Some of their characteristic features are found to agree with the predictions of an ensemble of random matrices suggested recently by Hikami and Zee. This result might be significant because it shows that there is a realistic physical system which is related to a non-Gaussian matrix ensemble. Far away from the center of the spectrum, for very small ΔE and very large N it is expected that the Gaussian unitary ensemble is identical to the Hikami-Zee ensemble, so that the pertinent spectrum can be described by both of them.