Identifying Non-Abelian Topological Order through Minimal Entangled States

Abstract

The topological order is equivalent to the pattern of long-range quantum entanglements, which cannot be measured by any local observable. Here we perform an exact diagonalization study to establish the non-Abelian topological order through entanglement entropy measurement. We focus on the quasiparticle statistics of the non-Abelian Moore-Read and Read-Rezayi states on the lattice boson models. We identify multiple independent minimal entangled states (MESs) in the groundstate manifold on a torus. The extracted modular $\mathcal{S}$ matrix from MESs faithfully demonstrates the Majorana quasiparticle or Fibonacci quasiparticle statistics, including the quasiparticle quantum dimensions and the fusion rules for such systems. These findings support that MESs manifest the eigenstates of quasiparticles for the non-Abelian topological states and encode the full information of the topological order.

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
• Fractional quantum Hall effect in the absence of Landau levels
• Identifying Topological Order by Entanglement Entropy
• Interacting anyons in topological quantum liquids: The golden chain
• Entanglement entropy in fermionic Laughlin states
• Characterizing topological order by studying the ground states of an infinite cylinder
• Numerical Analysis of Quasiholes of the Moore-Read Wavefunction
• Topological Entanglement Entropy from the Holographic Partition Function
• Degeneracy of non-abelian quantum Hall states on the torus: domain walls and conformal field theory
• Minimal Entangled States and Modular Matrix for Fractional Quantum Hall Effect in Topological Flat Bands
• Non-Abelian statistics as a Berry phase in exactly solvable models
• Establishing non-Abelian topological order in Gutzwiller projected Chern insulators via Entanglement Entropy and Modular S-matrix

Cited by in corpus (24)

• Interacting topological insulators: a review
• Diagrammatics for Bose condensation in anyon theories
• Edge theory approach to topological entanglement entropy, mutual information and entanglement negativity in Chern-Simons theories
• The Fractional Quantum Hall States at $\nu =13/5$ and $12/5$ and their Non-Abelian Nature
• Fractional charge pumping of interacting bosons in one-dimensional superlattice
• Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids
• Identification of a Kitaev Quantum Spin Liquid by Magnetic Field Angle Dependence
• Recent Developments in Fractional Chern Insulators
• Measuring space-group symmetry fractionalization in Z${}_2$ spin liquids
• Detecting and identifying 2D symmetry-protected topological, symmetry-breaking and intrinsic topological phases with modular matrices via tensor-network methods
• Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in $|C|=2$ flat bands
• Topological Characterization of Non-Abelian Moore-Read State using Density-Matrix Renormailzation Group
• Wave Functions for Fractional Chern Insulators on Disk Geometry
• Evolution of quantum entanglement with disorder in fractional quantum Hall liquids
• Possible non-Abelian Moore-Read state in double-layer bosonic fractional quantum Hall system
• Fibonacci anyon excitations of one-dimensional dipolar lattice bosons
• Non-Abelian Fractional Chern Insulator in Disk Geometry
• Microscopic Diagnosis of Universal Geometric Responses in Fractional Quantum Hall Liquids
• Full characterization of a spin liquid phase: from topological entropy to robustness and braid statistics
• Chiral conformal field theory for topological states and the anyon eigenbasis on the torus
• Fractional quantum Hall states with gapped boundaries in an extreme lattice limit
• Universal properties of the FQH state from the topological entanglement entropy and disorder effects
• Non-Abelian topological order with SO(5)${}_1$ chiral edge states
• An experimental algorithm for identifying the topological nature of Kondo and mixed valence insulators