Excitation spectrum and collective modes of composite fermions

According to the composite-fermion theory, the interacting electron system at filling factor ν is equivalent to the noninteracting composite-fermion system at ${\nu }^{\mathrm{*}}$=ν/(1-2mν), which in turn is related to the noninteracting electron system at ${\nu }^{\mathrm{*}}$. We show that several eigenstates of noninteracting electrons at ${\nu }^{\mathrm{*}}$ do not have any corresponding states for interacting electrons at ν, but, upon composite-fermion transformation, these states are eliminated, and the remaining states provide a good description of the spectrum at ν. We also show that the collective mode branches of incompressible states are well described as the collective modes of composite fermions. Our results suggest that, at small wave vectors, there is a single well-defined collective mode for all fractional quantum Hall states. Implications for the Chern-Simons treatment of composite fermions will be discussed.