Microscopic picture of a chiral Luttinger liquid: Composite fermion theory of edge states

We derive a microscopic theory of the composite fermions describing the low-lying edge excitations in the fractional quantum Hall liquid. Using the composite fermion transformation, one finds that the edge states of the (Formula presented) system in a disk sample are described by, in the one dimensional limit, the Calogero-Sutherland model with other interactions between the composite fermions as perturbations. It is shown that a large class of short-range interactions renormalize only the Fermi velocity while the exponent (Formula presented) is invariant under the condition of chirality. By taking the sharp edge potential into account, we obtain a microscopic justification of the chiral Luttinger liquid model of the fractional quantum Hall edge states. The approach applied to the (Formula presented) system can be generalized to the other edge states with odd denominator filling factors.