We describe solvable models that capture how impurity scattering in certain fractional quantum Hall edges can give rise to a neutral mode---i.e., an edge mode that does not carry electric charge. These models consist of two counterpropagating chiral Luttinger liquids together with a collection of discrete impurity scatterers. Our main result is an exact solution of these models in the limit of infinitely strong impurity scattering. From this solution, we explicitly derive the existence of a neutral mode and we determine all of its microscopic properties including its velocity. We also study the stability of the neutral mode and show that it survives at finite but sufficiently strong scattering. Our results are applicable to a family of Abelian fractional quantum Hall states of which the $\ensuremath{\nu}=2/3$ state is the most prominent example.
The elementary low energy excitations in the fractional quantum Hall (FQH) regime are known to be fractionally charged quasiparticles and quasiholes. This work focusses on quasiholes in a finite system of a few electrons treated by exact numerical diagonalization. Recent experimental [Chung et al., PRB 67, 201104 (2003)] and theoretical [Kane, Fisher, PRB 67, 045307 (2003)] work on quantum point contacts in the FQH regime showed strong evidence for single quasiparticle tunneling to be forbidden at low temperature. We want to gain insight into such constricted FQH systems by a numerical approach. Initially the basics of numerically treating a system in rectangular geometry and procedures to insert a quasihole excitation are presented. The excitations' stability and fractional charge is confirmed for different interactions. The question of quasihole tunneling is approached in two different systems: 1. A system posessing bound, localized states of a quasihole shows evidence for tunnel coupling between these states to exist. 2. Different potential forms to model a quantum point contact are investigated and the injection of a single quasihole near the constriction is surveyed in the system's time evolution.