Von Neumann Lattice Field Theory: Bloch Wave Basis and Wannier Function Basis in a Strong Magnetic Field
K. Ishikawa, N. Maeda, T. Ochiai, and H. Suzuki
Constructing useful sets of one-particle states in the quantum Hall system, we analyzed a Hall system subjected to a periodic potential and the Hall conductance. The Hall conductance is written by a winding number of the propagator. We also studied the Coulomb interaction effect and obtained a deep connection between the famous Hofstadter butterfly spectrum and the energy gap structure of the FQH states around the half filling.

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