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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