Microscopic construction of the chiral Luttinger liquid theory of the quantum Hall edge

Abstract

We give a microscopic derivation of the chiral Luttinger liquid theory $(\ensuremath{\chi}LL)$ for the Laughlin states. Starting from the wave function describing an arbitrary incompressibly deformed Laughlin state (IDLS) we quantize these deformations. In this way we obtain the low-energy projections of local microscopic operators and derive the quantum field theory of edge excitations directly from quantum mechanics of electrons. This shows that to describe experimental and numeric deviations from $\ensuremath{\chi}LL$ one needs to go beyond Laughlin's approximation. We show that in the large $N$ limit the IDLS is described by the dispersionless Toda hierarchy.