Exactly Soluble Model for Umklapp Scattering at Quantum-Hall Edges

TL;DR

This paper presents an exactly solvable model for Umklapp scattering at reconstructed quantum-Hall edges, revealing new interaction effects beyond traditional models and calculating correlation functions.

Contribution

It introduces a novel exactly solvable model that incorporates Umklapp processes in quantum-Hall edge excitations, extending beyond generalized Tomonaga-Luttinger theory.

Findings

Identifies a new Umklapp scattering process at quantum-Hall edges.

Provides exact solutions for the theory including Umklapp processes.

Calculates electronic correlation functions in the presence of these processes.

Abstract

We consider the low-energy, long-wave-length excitations of a reconstructed quantum-Hall edge where three branches of chiral one-dimensional edge excitations exist. We find that, in addition to forward scattering between the three edge-excitation branches, Coulomb interaction gives rise to a novel Umklapp-type scattering process that cannot be accounted for within a generalized Tomonaga-Luttinger model. We solve the theory including Umklapp processes exactly in the long-wave-length limit and calculate electronic correlation functions.