Fractional Quantum Hall Bilayers at Half-Filling: Tunneling-driven Non-Abelian Phase

Abstract

Multicomponent quantum Hall systems with internal degrees of freedom provide a fertile ground for the emergence of exotic quantum liquids. Here we investigate the possibility of non-Abelian topological order in the half-filled fractional quantum Hall (FQH) bilayer system driven by the tunneling effect between two layers. By means of the state-of-the-art density-matrix renormalization group, we unveil "finger print" evidence of the non-Abelian Moore-Read Pfaffian state emerging in the intermediate-tunneling regime, including the ground-state degeneracy on the torus geometry and the topological entanglement spectroscopy (entanglement spectrum and topological entanglement entropy) on the spherical geometry, respectively. Remarkably, the phase transition from the previously identified Abelian $(331)$ Halperin state to the non-Abelian Moore-Read Pfaffian state is determined to be continuous, which is signaled by the continuous evolution of the universal part of the entanglement spectrum, and discontinuities in the excitation gap and the derivative of the ground-state energy. Our results not only provide a "proof-of-principle" demonstration of realizing a non-Abelian state through coupling different degrees of freedom, but also open up a possibility in FQH bilayer systems for detecting different chiral $p-$wave pairing states.

18 pages, 11 figures

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• Fractional Quantum Hall State at Filling Factor $\nu =1/4$ in Ultra-High-Quality GaAs 2D Hole Systems
• Interface and Phase Transition between Moore-Read and Halperin 331 Fractional Quantum Hall States: Realization of Chiral Majorana Fermion
• Simple analog of the black-hole information paradox in quantum Hall interfaces
• Engineering Quantum Hall Phases in Synthetic Bilayer Graphene System
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• Anomalous Bilayer Quantum Hall Effect
• Strong interlayer charge transfer due to exciton condensation in an electrically-isolated GaAs quantum well bilayer
• Large Zeeman Splitting in Out-of-Plane Magnetic Field in a Double-Layer Quantum Point Contact
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
• Interlayer-correlated fractional quantum Hall state in a trilayer electron system
• Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene