Topological entanglement entropy in the second Landau level

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.

5 pages, 4 figures

References in corpus (8)

• Non-Abelian Anyons and Topological Quantum Computation
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Towards identification of a non-abelian state: observation of a quarter of electron charge at $\nu =5/2$ quantum Hall state
• Entanglement entropy in fermionic Laughlin states
• Topological Entanglement Entropy in the Quantum Dimer Model on the Triangular Lattice
• Finite Layer Thickness Stabilizes the Pfaffian State for the 5/2 Fractional Quantum Hall Effect: Wavefunction Overlap and Topological Degeneracy
• Bipartite entanglement entropy in fractional quantum Hall states
• Topological entropy of realistic quantum Hall wave functions

Cited by in corpus (5)

• Characterizing Neutral Modes of Fractional States in the Second Landau Level
• Abelian and Non-Abelian States in $\nu =2/3$ Bilayer Fractional Quantum Hall Systems
• ${\mathbb{Z}}_n$ superconductivity of composite bosons and the $7/3$ fractional quantum Hall effect
• Entanglement Measures for Quasi-Two-Dimensional Fractional Quantum Hall States
• Entanglement Entropy of Random Fractional Quantum Hall Systems