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

TL;DR

This paper derives the chiral Luttinger liquid theory for quantum Hall edges from a microscopic perspective, connecting wave functions of Laughlin states to edge excitations and revealing deviations from the ideal theory.

Contribution

It provides a microscopic derivation of the chiral Luttinger liquid theory from Laughlin wave functions and links edge dynamics to the dispersionless Toda hierarchy.

Findings

Derivation of edge theory from microscopic wave functions

Identification of deviations from ideal chiral Luttinger liquid behavior

Connection to the dispersionless Toda hierarchy in the large N limit

Abstract

We give a microscopic derivation of the chiral Luttinger liquid theory 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 chiral Luttinger liquid theory 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.