Universal properties of the FQH state from the topological entanglement entropy and disorder effects
arXiv:1511.00896 · doi:10.1016/j.aop.2017.07.005
Abstract
The topological entanglement entropy (TEE) is a robust measurement of the quantum many-body state with topological order. In fractional quantum Hall (FQH) state, it has a connection to the quantum dimension of the state itself and its quasihole excitations from the conformal field theory (CFT) description. We study the entanglement entropy (EE) in the Moore-Read (MR) and Read-Rezayi (RR) FQH states. The non-Abelian quasi- hole excitation induces an extra correction of the TEE which is related to its quantum dimension. With considering the effects of the disorder, the ground state TEE is stable before the spectral gap closing and the level statistics seems to have significant change with a stronger disorder, which indicates a many-body localization (MBL) transition.
12 pages, 7 figures, Annals of Physics, 2017
References in corpus (15)
- 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
- Fractional Quantum Hall States and Jack Polynomials
- Ground state entanglement and geometric entropy in the Kitaev's model
- Entanglement entropy in fermionic Laughlin states
- Infinite density matrix renormalization group for multicomponent quantum Hall systems
- Many body localization and thermalization: insights from the entanglement spectrum
- Fractional Quantum Hall Hierarchy and the Second Landau Level
- Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
- Bipartite entanglement entropy in fractional quantum Hall states
- Fractional quantum Hall effect at : Ground states, non-Abelian quasiholes, and edge modes in a microscopic model
- Properties of Non-Abelian Fractional Quantum Hall States at Filling
- Correlation Lengths and Topological Entanglement Entropies of Unitary and Non-Unitary Fractional Quantum Hall Wavefunctions
- Floquet Thermalization: Symmetries and Random Matrix Ensembles
- Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids