Non-Abelian Quantum Hall Effect in Topological Flat Bands

Abstract

Inspired by recent theoretical discovery of robust fractional topological phases without a magnetic field, we search for the non-Abelian quantum Hall effect (NA-QHE) in lattice models with topological flat bands (TFBs). Through extensive numerical studies on the Haldane model with three-body hard-core bosons loaded into a TFB, we find convincing numerical evidence of a stable $\nu =1$ bosonic NA-QHE, with the characteristic three-fold quasi-degeneracy of ground states on a torus, a quantized Chern number, and a robust spectrum gap. Moreover, the spectrum for two-quasihole states also shows a finite energy gap, with the number of states in the lower energy sector satisfying the same counting rule as the Moore-Read Pfaffian state.

5 pages, 7 figures

References in corpus (19)

• 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
• Fractional quantum Hall effect in the absence of Landau levels
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• An exact chiral spin liquid with non-Abelian anyons
• Fractional Quantum Hall States and Jack Polynomials
• Finite Layer Thickness Stabilizes the Pfaffian State for the 5/2 Fractional Quantum Hall Effect: Wavefunction Overlap and Topological Degeneracy
• Abelian and Non-abelian Hall Liquids and Charge Density Wave: Quantum Number Fractionalization in One and Two Dimensions
• Non-Abelian Statistics in a Quantum Antiferromagnet
• The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus
• Emerging Bosons with Three-Body Interactions from Spin-1 Atoms in Optical Lattices
• Topological properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros
• A classification of symmetric polynomials of infinite variables -- a construction of Abelian and non-Abelian quantum Hall states
• Spontaneous Particle-Hole Symmetry Breaking in the $\nu =5/2$ Fractional Quantum Hall Effect
• Pfaffian-like ground state for 3-body-hard-core bosons in 1D lattices

Cited by in corpus (94)

• Topological Flat Band Models and Fractional Chern Insulators
• Fractional Quantum Hall Physics in Topological Flat Bands
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Topological Nematic States and Non-Abelian Lattice Dislocations
• Exotic electronic states in the world of flat bands: from theory to material
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Topological flat band models with arbitrary Chern numbers
• Reaching Fractional Quantum Hall States with Optical Flux Lattices
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Series of Abelian and Non-Abelian States in C>1 Fractional Chern Insulators
• Flat bands with higher Chern number in pyrochlore slabs
• Spectral and transport properties of the two-dimensional Lieb lattice
• Hierarchy of fractional Chern insulators and competing compressible states
• Induced self-stabilization in fractional quantum Hall states of light
• Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators
• The impossibility of exactly flat non-trivial Chern bands in strictly local periodic tight binding models
• Topology and Interactions in a Frustrated Slab: Tuning from Weyl Semimetals to C > 1 Fractional Chern Insulators
• Non-Abelian topological insulators from an array of quantum wires
• Enhancing the stability of a fractional Chern insulator against competing phases
• Pseudopotential Formalism for Fractional Chern Insulators
• Fractional Chern Insulators beyond Laughlin states
• Quantum field theory on toroidal topology: algebraic structure and applications
• Adiabatic continuity between Hofstadter and Chern insulator states
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Superfluidity of Bosons in Kagome Lattices with Frustration
• Non-Abelian Fractional Chern Insulators from Long-Range Interactions
• From fractional Chern insulators to Abelian and non-Abelian fractional quantum Hall states: adiabatic continuity and orbital entanglement spectrum
• ${\mathbb{Z}}_2$ fractional topological insulators in two dimensions
• Haldane Statistics for Fractional Chern Insulators with an Arbitrary Chern number
• Fractional charge pumping of interacting bosons in one-dimensional superlattice
• Minimal Entangled States and Modular Matrix for Fractional Quantum Hall Effect in Topological Flat Bands
• Higher Landau-Level Analogs and Signatures of Non-Abelian States in Twisted Bilayer MoTe${}_2$
• Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models
• Establishing non-Abelian topological order in Gutzwiller projected Chern insulators via Entanglement Entropy and Modular S-matrix
• Recent Developments in Fractional Chern Insulators
• Bulk-edge correspondence in fractional Chern insulators
• Chiral spin density wave, spin-charge-Chern liquid and d+id superconductivity in 1/4-doped correlated electronic systems on the honeycomb lattice
• Tunable Band Topology Reflected by Fractional Quantum Hall States in Two-Dimensional Lattices
• Wigner crystallization in topological flat bands
• Bosonic Pfaffian State in the Hofstadter-Bose-Hubbard Model
• Characterization of quasiholes in fractional Chern insulators
• Fractional Topological Phases in Generalized Hofstadter Bands with Arbitrary Chern Numbers
• Fractional Chern Insulator phase at the transition between checkerboard and Lieb lattice
• Identifying Non-Abelian Topological Order through Minimal Entangled States
• Two-component quantum Hall effects in topological flat bands
• Quantum phases of disordered flatband lattice fractional quantum Hall systems
• Zero modes, Bosonization and Topological Quantum Order: The Laughlin State in Second Quantization
• Topological Characterization of Non-Abelian Moore-Read State using Density-Matrix Renormailzation Group
• Edge Excitations in Fractional Chern Insulators
• Momentum-space instantons and maximally localized flat-band topological Hamiltonians
• Algebraic approach to the study of zero modes of Haldane pseudopotentials
• Bosonic integer quantum Hall states in topological bands with Chern number two
• SU(N) fractional quantum Hall effects in topological flat bands
• 3- and 4-body Interactions from 2-body interactions in Spin Models: A Route to Abelian and Non-Abelian Fractional Chern Insulators
• Crystal-symmetry preserving Wannier states for fractional chern insulators
• Frustrated extended Bose-Hubbard model and deconfined quantum critical points with optical lattices at the anti-magic wavelength
• Elementary formula for the Hall conductivity of interacting systems
• Chern Insulators on Singular Geometries
• Fractional Chern Insulators in Singular Geometries
• Topological Phenomena in Trapped Ion Systems
• Exotic Fractional Topological States in Two-Dimensional Organometallic Material
• Anisotropic Quantum Spin Hall Effect, Spin-Orbital Textures and Mott Transition
• Wave Functions for Fractional Chern Insulators on Disk Geometry
• Long-lived Topological Flatband Excitons in Semiconductor Moiré Heterostructures: a Bosonic Kane-Mele Model Platform
• $Z_2$ fractionalized Chern/topological insulators in an exactly soluble correlated model
• Possible non-Abelian Moore-Read state in double-layer bosonic fractional quantum Hall system
• Magnetic translation algebra with or without magnetic field in the continuum or on arbitrary Bravais lattices in any dimension
• Hyperbolic Fractional Chern insulators
• Interacting bosons in two-dimensional flat band systems
• Fractional Topological States in Quantum Spin Chains with Periodical Modulation
• Intertwined Order in Fractional Chern Insulators from Finite-Momentum Pairing of Composite Fermions
• Non-Abelian Fractional Chern Insulators and Competing States in Flat Moiré Bands
• Non-Abelian Fractional Chern Insulator in Disk Geometry
• Fermionic non-Abelian fractional Chern insulators from dipolar interactions
• Chern number matrix of the non-Abelian spin-singlet fractional quantum Hall effect
• Bosonic fractional Chern insulating state at integer fillings in multi-band system
• Exact Topological Flat Bands from Continuum Landau Levels
• Phase transitions of bosonic fractional quantum Hall effect in topological flat bands
• Invariance of topological indices under Hilbert space truncation
• Fractional quantum anomalous Hall phase for Raman superarray of Rydberg atoms
• Fractional quantum Hall states with gapped boundaries in an extreme lattice limit
• Non-Abelian chiral spin liquid on spin-1 kagome lattice: truncation of an exact Hamiltonian and numerical optimization
• Interband excitations in the 1D limit of two-band fractional Chern insulators
• Anomalous Bilayer Quantum Hall Effect
• Universal intrinsic orbital dynamics from Berry curvature in electronic two-band systems
• How quantum fluctuations freeze a classical liquid and then melt it into a topological one
• On the geometrical description of fractional Chern insulators based on static structure factor calculations
• Chiral spin liquid from magnetic Wannier states
• Bosonic Halperin fractional quantum Hall effect at filling factor $\nu =2/5$
• Exact Mappings in Condensed Matter Physics
• Disorder effects in two-dimensional flat-band system with next-nearest-neighbor hopping
• Experimental Proposal on Non-Abelian Aharonov-Bohm Caging Effect with a Single Trapped Ion