Topological entanglement entropy in the second Landau level

TL;DR

This study investigates the topological entanglement entropy in second Landau level quantum Hall states, providing insights into their topological order through numerical analysis and finite thickness corrections.

Contribution

It presents the first direct diagonalization analysis of topological entanglement entropy for specific quantum Hall states in the second Landau level.

Findings

Nu=7/3 state aligns with the k=4 Read-Rezayi topological entropy

Finite thickness effects significantly influence entanglement entropy calculations

Nu=12/5 results are inconclusive regarding topological order

Abstract

The entanglement entropy of the incompressible states of a realistic quantum Hall system in the second Landau level are studied by direct diagonalization. The subdominant term to the area law, the topological entanglement entropy, which is believed to carry information about topologic order in the ground state, was extracted for filling factors nu = 12/5 and nu = 7/3. While it is difficult to make strong conclusions about nu = 12/5, the nu = 7/3 state appears to be very consistent with the topological entanglement entropy for the k=4 Read-Rezayi state. The effect of finite thickness corrections to the Coulomb potential used in the direct diagonalization are also systematically studied.