Possible non-Abelian Moore-Read state in double-layer bosonic fractional quantum Hall system

Abstract

Identifying and understanding interacting systems that can host non-Abelian topological phases with fractionalized quasiparticles have attracted intense attentions in the past twenty years. Theoretically, it is possible to realize a rich variety of such states by coupling two Abelian fractional quantum Hall (FQH) states together through gapping out part of the low energy degrees of freedom. So far, there are some indications, but no robust example has been established in bilayer systems for realizing the non-Abelian state in the past. Here, we present a phase diagram of a double-layer bosonic FQH system based on the exact diagonalization and density-matrix renormalization group (DMRG) calculations, which demonstrate a potential regime with the emergence of the non-Abelian bosonic Moore-Read state. We start from the Abelian phase with fourfold topological degeneracies on torus geometry when the two layers are weakly coupled. With the increase of interlayer tunneling, we find an intermediate regime with a threefold groundstate degeneracy and a finite fractional drag Hall conductance. We find the different topological sectors in consistent with Moore-Read state by inserting different fluxes in adiabatic DMRG study. We also extract the modular $\mathcal{S}-$ matrix, which supports the emergence of the non-Abelian Ising anyon quasiparticle in this system.

7 figures; 7 pages

References in corpus (16)

• 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
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Fractional quantum Hall effect in the absence of Landau levels
• Characterizing topological order by studying the ground states of an infinite cylinder
• Topological Entanglement Entropy from the Holographic Partition Function
• Fibonacci Anyons From Abelian Bilayer Quantum Hall States
• Flux insertion, entanglement, and quantized responses
• Competing Abelian and non-Abelian topological orders in $\nu =1/3+1/3$ quantum Hall bilayers
• Fractional quantum Hall effects in bilayers in the presence of inter-layer tunneling and charge imbalance
• Bridge between Abelian and Non-Abelian Fractional Quantum Hall States
• Establishing non-Abelian topological order in Gutzwiller projected Chern insulators via Entanglement Entropy and Modular S-matrix
• Bilayer mapping of the paired quantum Hall state: Instability toward anisotropic pairing

Cited by in corpus (13)

• Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in $\nu =1/2+1/2$ Bilayers
• Topological Characterization of Non-Abelian Moore-Read State using Density-Matrix Renormailzation Group
• Non-Abelian phases in two-component $\nu =2/3$ fractional quantum Hall states: Emergence of Fibonacci anyons
• Landau-Ginzburg Theories of Non-Abelian Quantum Hall States from Non-Abelian Bosonization
• Projective construction of the ${\mathbb{Z}}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry
• Determining non-Abelian topological order from infinite projected entangled pair states
• Determining topological order from infinite projected entangled pair states
• Phase diagram of $\nu =\frac{1}{2}+\frac{1}{2}$ bilayer bosons with inter-layer couplings
• Chern number matrix of the non-Abelian spin-singlet fractional quantum Hall effect
• Even-denominator fractional quantum Hall state in conventional triple-gated quantum point contact
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Bosonic Halperin fractional quantum Hall effect at filling factor $\nu =2/5$
• Variational methods for characterizing matrix product operator symmetries