Topological entropy of realistic quantum Hall wave functions

TL;DR

This paper investigates the topological entanglement entropy of quantum Hall states through numerical diagonalization, confirming theoretical predictions for certain filling factors and providing insights into their topological order.

Contribution

It provides the first direct numerical extraction of topological entanglement entropy for realistic quantum Hall wave functions at specific filling factors.

Findings

Topological entanglement entropy matches Laughlin wave function predictions at 1/3 and 1/5.

At 5/2, the entropy aligns with the Moore-Read wave function.

Results support the topological nature of these quantum Hall states.

Abstract

The entanglement entropy of the incompressible states of a realistic quantum Hall system 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 1/3, 1/5 and 5/2. The results for 1/3 and 1/5 are consistent with the topological entanglement entropy for the Laughlin wave function. The 5/2 state exhibits a topological entanglement entropy consistent with the Moore-Read wave function.