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The Hall conductance ₗₘ of two-dimensional lattice electrons in a random potential is investigated. The randomness induces a quantum phase transition where the sum rule of ₗₘ plays an important role. Using the string (anyon) gauge, numerical study becomes possible in sufficiently weak magnetic fields essential to the floating scenario in the continuum model. Topological objects in the Bloch wave functions (charged vortices) are obtained explicitly. Anomalous plateau transitions (ₗₘ0ex{0ex}=0ex{0ex}2, 3, >1) and the trajectory of delocalized states are discussed as well.
Hatsugai et al. (Mon,) studied this question.