Fractional quantum Hall bilayers at half filling: Tunneling-driven non-Abelian phase

2016/08/28 by W. Zhu, Zhao Liu, F. D. M. Haldane +1
Mathematics · Physics and Astronomy · #Condensed matter physics #Electron #Ground state #Mathematics #Pfaffian #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum entanglement #Quantum mechanics #Quantum phase transition #Symmetry protected topological order #Topological Materials and Phenomena #Topological degeneracy #Topological order #Topology (electrical circuits) #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.94.245147

published as Phys. Rev. B 94, 245147 (2016) · 18 pages, 11 figures

arxiv created 2016/08/28 · openalex publication_date 2016/12/30 · arxiv updated 2017/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

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 ``fingerprint'' 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\text\ensuremath-wave pairing states.

Citations

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