Wave-function and level statistics of random two-dimensional gauge fields.

Abstract

Level and wave-function statistics have been studied for two-dimensional clusters of the square lattice in the presence of random magnetic fluxes. Fluxes traversing lattice plaquettes are distributed uniformly between -1/2${\mathrm{\ensuremath{\Phi}}}_{0}$ and 1/2${\mathrm{\ensuremath{\Phi}}}_{0}$ with ${\mathrm{\ensuremath{\Phi}}}_{0}$ the flux quantum. All considered statistics start close to the corresponding Wigner-Dyson distribution for small system sizes and monotonically move towards Poisson statistics as the cluster size increases. Scaling is quite rapid for states close to the band edges but really difficult to observe for states well within the band. Localization properties are discussed considering two different scenarios. Experimental measurement of one of the considered statistics---wave-function statistics seems the most promising one---could discern between both possibilities. A real version of the previous model, i.e., a system that is invariant under time reversal, has been studied concurrently to get coincidences and differences with the Hermitian model. \textcopyright{} 1996 The American Physical Society.