Entanglement Entropy of Random Fractional Quantum Hall Systems

Abstract

The entanglement entropy of the $\nu =1/3$ and $\nu =5/2$ quantum Hall states in the presence of short range random disorder has been calculated by direct diagonalization. A microscopic model of electron-electron interaction is used, electrons are confined to a single Landau level and interact with long range Coulomb interaction. For very weak disorder, the values of the topological entanglement entropy are roughly consistent with expected theoretical results. By considering a broader range of disorder strengths, the fluctuation in the entanglement entropy was studied in an effort to detect quantum phase transitions. In particular, there is a clear signature of a transition as a function of the disorder strength for the $\nu =5/2$ state. Prospects for using the density matrix renormalization group to compute the entanglement entropy for larger system sizes are discussed.

29 pages, 16 figures; fixed figures and figure captions; revised fluctuation calculations

References in corpus (14)

• 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
• Quantum Noise as an Entanglement Meter
• Entanglement entropy in fermionic Laughlin states
• Topological Entanglement Renyi Entropy and Reduced Density Matrix Structure
• The entanglement gap and a new principle of adiabatic continuity
• Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
• Bipartite entanglement entropy in fractional quantum Hall states
• Topological Entanglement Entropy from the Holographic Partition Function
• Quantum noise and entanglement generated by a local quantum quench
• Entanglement signatures of quantum Hall phase transitions
• Entanglement Scaling of Fractional Quantum Hall states through Geometric Deformations
• Skyrmions in the Moore-Read state at nu=5/2
• Topological Entropy of Quantum Hall States in Rotating Bose Gases

Cited by in corpus (6)

• Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids
• Focus on topological quantum computation
• Evolution of quantum entanglement with disorder in fractional quantum Hall liquids
• Short and Long Ranged Impurities in Fractional Quantum Hall Systems
• Stability of Fractional Quantum Hall States in Disordered Photonic Systems
• Disorder-driven phase transitions in bosonic fractional quantum Hall liquids