Non-Abelian topological order with SO(5)${}_1$ chiral edge states

Abstract

We consider a chiral spin liquid constructed using the parton theory. This state supports non-Abelian anyons and neutral fermions, which share some similarities with the celebrated Moore-Read state. The edge physics of the parton state and the Moore-Read state is very different. Based on conformal field theory (CFT) analysis, it is proposed that the edge states exhibit an emergent SO(5) symmetry. The counting of edge states in the low-lying SO(5)${}_1$ CFT towers is computed. The chiral spin liquid is generated using tensor network methods, which allows us to confirm the SO(5)${}_1$ counting using entanglement spectrum. An additional feature of multiple branches in the entanglement spectrum is observed and analyzed.

References in corpus (60)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Quantum Spin Liquids
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Quantum Spin Liquid States
• Topological orders and Edge excitations in FQH states
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• A Four Dimensional Generalization of the Quantum Hall Effect
• Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state
• Fractional statistics in anyon collisions
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Electron correlation in the second Landau level; a competition between many, nearly degenerate quantum phases
• Robust fractional quantum Hall states and continuous quantum phase transitions in a half-filled bilayer graphene Landau level
• Characterizing topological order by studying the ground states of an infinite cylinder
• Topological flat band models with arbitrary Chern numbers
• New Class of Non-Abelian Spin-Singlet Quantum Hall States
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
• Even denominator fractional quantum Hall state in bilayer graphene
• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• Observation of even denominator fractional quantum Hall effect in suspended bilayer graphene
• Flat bands with higher Chern number in pyrochlore slabs
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Even denominator fractional quantum Hall states in higher Landau levels of graphene
• Momentum polarization: an entanglement measure of topological spin and chiral central charge
• The Ground State Structure and Modular Transformations of Fractional Quantum Hall States on a Torus
• Microscopic models for Kitaev's sixteenfold way of anyon theories
• One Proximate Kitaev Spin Liquid in the $K$-$J$-$\Gamma$ Model on the Honeycomb Lattice
• Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
• A Stable Pfaffian State in Bilayer Graphene
• Non-Abelian quantized Hall states of electrons at filling factors 12/5 and 13/5 in the first excited Landau level
• Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
• Topological Phases in the Zeroth Landau Level of Bilayer Graphene
• Prediction of a non-Abelian fractional quantum Hall state with $f$-wave pairing of composite fermions in wide quantum wells
• Projected BCS states and spin Hamiltonians for the SO(n)_1 Wess-Zumino-Witten model
• Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models
• Tensor network representations of parton wave functions
• Lattice spin models for non-Abelian Chiral Spin Liquids
• Valence bond solid states with symplectic symmetry
• Topologically distinct classes of valence bond solid states with their parent Hamiltonians
• Establishing non-Abelian topological order in Gutzwiller projected Chern insulators via Entanglement Entropy and Modular S-matrix
• Finite and Infinite Matrix Product States for Gutzwiller Projected Mean-Field Wavefunctions
• ${\mathbb{Z}}_n$ superconductivity of composite bosons and the $7/3$ fractional quantum Hall effect
• Efficient tensor network representation for Gutzwiller projected states of paired fermions
• Identifying Non-Abelian Topological Order through Minimal Entangled States
• Non-Abelian Chiral Spin Liquid on the Kagome Lattice
• Local two-body parent Hamiltonians for the entire Jain sequence
• Matrix product states for Hartree-Fock-Bogoliubov wave functions
• Real-space entanglement spectra of parton states in fractional quantum Hall systems
• A hierarchy of exactly solvable spin-1/2 chains with so(N)_1 critical points
• Identifying non-Abelian topological ordered state and transition by momentum polarization
• Spin Correlations and Topological Entanglement Entropy in a Non-Abelian Spin-1 Spin Liquid
• Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus
• Chiral conformal field theory for topological states and the anyon eigenbasis on the torus
• An Exactly Solvable Model for Strongly Interacting Electrons in a Magnetic Field

Cited by in corpus (1)

• Chiral spin liquids with projected Gaussian fermionic entangled pair states