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Delocalization of electrons in a Random Magnetic Field

Delocalization problem for a two-dimensional non-interacting electron system is studied under a random magnetic field. With the presence of a random magnetic field, the Hall conductance carried by each eigenstate can become nonzero and quantized in units of $e^2/h$. Extended states are characterized by nonzero Hall conductance, and by studying finite-size scaling of the density of extended states, an insulator-metal phase transition is revealed. The metallic phase is found at the center of energy band which is separated from the localized states at the band tails by critical energies $\pm E_c$. Both localization exponent and the critical energy $E_c$ are shown to be dependent on the strength of random magnetic field.