Universality of the edge tunneling exponent of fractional quantum Hall liquids

TL;DR

This paper investigates the universality of the edge tunneling exponent in fractional quantum Hall liquids, showing that edge sharpness and confinement influence the tunneling behavior, reconciling previous conflicting calculations.

Contribution

The study demonstrates that edge reconstruction effects, driven by edge sharpness and confinement, are key to understanding the universality of tunneling exponents in fractional quantum Hall states.

Findings

Edge Green's function calculated via exact diagonalization.

Edge reconstruction affects tunneling exponent.

Coulomb interaction influences edge sharpness and confinement effects.

Abstract

Recent calculations of the edge tunneling exponents in quantum Hall states appear to contradict their topological nature. We revisit this issue and find no fundamental discrepancies. In a microscopic model of fractional quantum Hall liquids with electron-electron interaction and confinement, we calculate the edge Green's function via exact diagonalization. Our results for $\nu = 1/3$ and 2/3 suggest that in the presence of Coulomb interaction, the sharpness of the edge and the strength of the edge confining potential, which can lead to edge reconstruction, are the parameters that are relevant to the universality of the electron tunneling I-V exponent.