Microscopic description of the chiral Tomonaga-Luttinger liquid at the fractional quantum Hall edge

TL;DR

This paper reformulates the effective field theory of fractional quantum Hall edges from microscopic principles, deriving a chiral Tomonaga-Luttinger liquid with interactions and confirming its predictions with experimental data.

Contribution

It introduces a microscopic derivation of the chiral Tomonaga-Luttinger liquid theory for fractional quantum Hall edges, including interaction effects and tunneling exponents.

Findings

Derived a constrained chiral TLL theory from microscopic electron dynamics.

Calculated one-loop corrections matching experimental tunneling exponents.

Linked noncommutative Chern-Simons theory to edge state descriptions.

Abstract

The effective field theory of the fractional quantum Hall edge is reformulated from microscopic dynamics. Noncommutative Chern-Simons theory is a microscopic description for the quantum Hall fluid. We use it for reference. Considering relabeling symmetry of the electrons and incompressibility of the fluid, we obtain a constraint and derive a chiral Tomonaga-Luttinger liquid theory containing interaction terms. We calculate one-loop corrections to the phonon and electron propagators and get a new tunneling exponent. It agrees with experiments.