Electron hopping in the presence of random flux

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Abstract
We calculate the distribution of single-particle states for a spinless electron hopping on a two-dimensional square lattice in the presence of random magnetic flux. The flux is taken to be uniformly random between 0 and 1 flux quantum, taking on either continuous or rational values. We consider nearest-neighbor and next-nearest-neighbor hopping. Compared with the density of states without flux, the allowed energies span a smaller range, and the distribution is relatively flat. If states are filled with noninteracting fermions, the random flux lowers the energy for a wide range of filling fractions and next-nearest-neighbor couplings. Examination of the wave functions shows that most of the states are extended with a tail of localized states near the band edge.