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

Abstract

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 $\ensuremath{\nu}=1/m$ 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 $g=\ensuremath{\nu}=1/m$ 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 $\ensuremath{\nu}=1/m$ system can be generalized to the other edge states with odd denominator filling factors.