Multicomponent quantum Hall systems with internal degrees of freedom providea fertile ground for the emergence of exotic quantum liquids. Here weinvestigate the possibility of non-Abelian topological order in the half-filledfractional quantum Hall (FQH) bilayer system driven by the tunneling effectbetween two layers. By means of the state-of-the-art density-matrixrenormalization group, we unveil "finger print" evidence of the non-AbelianMoore-Read Pfaffian state emerging in the intermediate-tunneling regime,including the ground-state degeneracy on the torus geometry and the topologicalentanglement spectroscopy (entanglement spectrum and topological entanglemententropy) on the spherical geometry, respectively. Remarkably, the phasetransition from the previously identified Abelian $(331)$ Halperin state to thenon-Abelian Moore-Read Pfaffian state is determined to be continuous, which issignaled by the continuous evolution of the universal part of the entanglementspectrum, and discontinuities in the excitation gap and the derivative of theground-state energy. Our results not only provide a "proof-of-principle"demonstration of realizing a non-Abelian state through coupling differentdegrees of freedom, but also open up a possibility in FQH bilayer systems fordetecting different chiral $p-$wave pairing states.
展开▼
