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.

Landau-Ginzburg theories of non-Abelian quantum Hall states from non-Abelian bosonization

“…Such projections have been implemented at the formal level of the edge CFT ("ideal") wave function [40,41] and in coupled wire constructions [42,43]. Numerical studies of bilayer systems have also lent support to this idea [44][45][46][47][48][49][50]. However, a robust bulk LG description of generic non-Abelian FQH states continues to be lacking.…”

Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians

“…There are two generators for the four quasihole braid group, giving rise to two different braids, which do not commute with each other and hence forming non-Abelian statistics. Here, Q = 4 and hence there are two conformal blocks for (6) which give rise to the degeneracy. We denote the conformal block indices as m I = 0 and m ψ = 1.…”

“…The fractional quantum Hall effect was a pioneering breakthrough in the context of topological systems [1][2][3][4] . This phenomenon unveils an exotic phase of matter [5][6][7][8][9][10][11][12][13][14][15][16] and is obtainable at very low temperatures.…”

Unconventional Anisotropic Even-Denominator Fractional Quantum Hall State in a System with Mass Anisotropy

“…A hallmark of a high-quality, interacting twodimensional electron system (2DES) is the mysterious even-denominator fractional quantum Hall state (FQHS) [1][2][3][4][5][6][7], which is expected to harbor Majorana excitations obeying non-Abelian statistics and be of potential use in topological quantum computing [8][9][10][11]. Here we expose some remarkable properties of this state in a 2DES, confined to an AlAs quantum well, where the electrons possess an anisotropic in-plane effective mass.…”