Topological entropy of realistic quantum Hall wave functions

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.

6 pages, 6 figures; improved computations and graphics; added references

References in corpus (8)

• Entanglement entropy in fermionic Laughlin states
• Topological Entanglement Entropy in the Quantum Dimer Model on the Triangular Lattice
• Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
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• Topological Entanglement Entropy from the Holographic Partition Function
• Edge Excitations and Non-Abelian Statistics in the Moore-Read State: A Numerical Study in the Presence of Coulomb Interaction and Edge Confinement
• Understanding the 5/2 Fractional Quantum Hall Effect without the Pfaffian Wave Function
• Numerical studies of the Pfaffian model of the nu=5/2 fractional quantum Hall effect

Cited by in corpus (16)

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• Entanglement entropy of integer Quantum Hall states
• Entanglement signatures of quantum Hall phase transitions
• Entanglement Scaling of Fractional Quantum Hall states through Geometric Deformations
• Rényi entanglement entropies in quantum dimer models : from criticality to topological order
• Entanglement entropy of integer Quantum Hall states in polygonal domains
• Topological Order and Degenerate Singular Value Spectrum in Two-Dimensional Dimerized Quantum Heisenberg Model
• Entanglement Measures for Quasi-Two-Dimensional Fractional Quantum Hall States
• Dynamics and level statistics of interacting fermions in the Lowest Landau Level
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Topological Entropy of Quantum Hall States in Rotating Bose Gases
• Transition of a ${\mathbb{Z}}_3$ topologically ordered phase to trivial and critical phases
• Entanglement Entropy of Random Fractional Quantum Hall Systems
• Topological entanglement entropy in the second Landau level
• Entanglement Chern number for three-dimensional topological insulators: Characterization by Weyl points of entanglement Hamiltonians
• Topological entanglement entropy for torus knot bipartitions and the Verlinde-like formulas