Density matrix renormalization group study of the $\nu=1/3$ edge states in fractional quantum Hall systems

TL;DR

This study uses the density matrix renormalization group method to analyze the edge states in fractional quantum Hall systems at filling factor 1/3, revealing how boundary conditions and potential shape affect edge structure and stability.

Contribution

It demonstrates the application of DMRG to fractional quantum Hall edge states and uncovers the emergence of counterpropagating edge channels with changing chemical potential.

Findings

Edge density oscillations relate to magnetoroton excitations.

Counterpropagating edge channels appear with chemical potential variation.

Bulk states remain incompressible despite edge state changes.

Abstract

The edge states in the fractional quantum Hall systems at filling factor $\nu=1/3$ are studied by the density matrix renormalization group method. It is shown that the density oscillation induced by the local boundary condition at the edge is characterized by the wave number of the minimum magnetoroton excitation, and this structure is partially reconstructed with the change in the confinement potential shape. In particular, the $\nu=1$ counterpropagating edge channel appears with the change in the chemical potential, which is consistent with recent experiments on heat transport. The stability of the bulk states against the change in the number of electrons confirms that the bulk part of the fractional quantum Hall state is incompressible, while the edge state is compressible.