Chiral Luttinger liquid and the edge excitations in the fractional quantum Hall states

The edge excitations are shown to form a new kind of state which is called the Chiral Luttinger Liquid (´LL), which clearly demonstrate the non-Fermi liquid behaviors of the FQH states.

Abstract

The low-energy effective theory of the edge excitations in the fractional quantum Hall (FQH) states is derived. The edge excitations are shown to form a new kind of state which is called the chiral Luttinger liquid (\ensuremath{\chi}LL). The effective theory is exactly soluble. This enables us to easily calculate all the low-energy properties of the edge excitations. We calculate the electron propagator and the spectral function, which clearly demonstrate the non-Fermi-liquid behaviors of the \ensuremath{\chi}LL. We also calculate the interference effects between excitations on different edges. We demonstrate that the properties of the edge excitations are closely related to the properties of the FQH states on compacted spaces. Thus the properties of the edge excitations can be used to characterize the topological orders in the FQH states. We also show that the FQH states with filling fractions \ensuremath{\nu}\ensuremath{\ne}1/l must have at least two branches of edge excitations.