Composite fermions in the half-filled lowest Landau level: a macroscopic justification
F. Evers
Abstract
An effective Hamiltonian for spinless electrons in the lowest Landau level (LLL) close to half filling is derived. As opposed to the treatment in standard Chern-Simons theories (CS) we first project to the LLL and only then apply a CS-transformation on the Hamiltonian. The transformed field operators act in the lowest Landau level only and have fermionic commutation relations for small wavenumbers ignoring gauge field fluctuations. When acting on the Hamiltonian at half filling the gauge transformation removes the monopole term in the interaction and does not eliminate the magnetic field.
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