Many-body study of a quantum point contact in the fractional quantum Hall regime at v=5/2

TL;DR

This paper investigates the edge modes and tunneling behaviors of a quantum point contact in the fractional quantum Hall regime at filling factor 5/2, revealing insights into non-Abelian states and their scaling properties.

Contribution

It provides a detailed analysis of edge excitations and tunneling in the Moore-Read Pfaffian state using exact diagonalization and Monte Carlo methods, highlighting the neutral and charged velocity equality.

Findings

Identification of conformal towers including non-Abelian sectors.

Calculation of scaling exponents for edge modes.

Equality of neutral and charged velocities in the Pfaffian state.

Abstract

We study a quantum point contact in the fractional quantum Hall regime at Landau level filling factors 1/3 and 5/2. By using exact diagonalizations in the cylinder geometry we identify the edge modes in the presence of a parabolic confining potential. By changing the sign of the potential we can access both the tunneling through the bulk of the fluid and the tunneling between spatially separated droplets. This geometry is realized in the quantum point contact geometry for two-dimensional electron gases. In the case of the model Moore-Read Pfaffian state at filling factor 5/2 we identify the conformal towers of many-body eigenstates including the non-Abelian sector. By a Monte-Carlo technique we compute the various scaling exponents that characterize the edge modes. In the case of hard-core interactions whose ground states are exact model wavefunction we find equality of neutral and charged velocities for the Pfaffian state both bosonic and fermionic.