Parent Hamiltonian for the non-Abelian chiral spin liquid

Abstract

We construct a parent Hamiltonian for the family of non-Abelian chiral spin liquids proposed recently by two of us [PRL 102, 207203 (2009)], which includes the Abelian chiral spin liquid proposed by Kalmeyer and Laughlin, as the special case S=1/2. As we use a circular disk geometry with an open boundary, both the annihilation operators we identify and the Hamiltonians we construct from these are exact only in the thermodynamic limit.

5+2 pages, no figures. Version 2: two references added

References in corpus (16)

• Non-Abelian Anyons and Topological Quantum Computation
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• An exact chiral spin liquid with non-Abelian anyons
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Topological Entanglement Entropy of Z2 Spin liquids and Lattice Laughlin states
• Laughlin spin liquid states on lattices obtained from conformal field theory
• Quantum spin Hamiltonians for the SU(2)_k WZW model
• Non-Abelian Braiding of Lattice Bosons
• Spin liquid phase in a $S=1/2$ quantum magnet on the kagome lattice
• Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
• Fractional spin liquid hierarchy for spin S antiferromagnets
• Generalizations of Perelomov's identity on the completeness of coherent states

Cited by in corpus (70)

• Spin liquid nature in the Heisenberg $J_1$-$J_2$ triangular antiferromagnet
• Wire deconstructionism of two-dimensional topological phases
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Thirty Years of Composite Fermions and Beyond
• Projective symmetry group classification of chiral spin liquids
• Fractional quantum Hall states in lattices: Local models and physical implementation
• Band structure engineering of ideal fractional Chern insulators
• Coupled wire construction of chiral spin liquids
• Nature of chiral spin liquids on the kagome lattice
• A Quantum Dipolar Spin Liquid
• Computational inverse method for constructing spaces of quantum models from wave functions
• Four-Spin Terms and the Origin of the Chiral Spin Liquid in Mott Insulators on the Triangular Lattice
• Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
• Chiral Spin Liquids in Arrays of Spin Chains
• Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
• Emergence of Chiral Spin Liquids via Quantum Melting of Non-Coplanar Magnetic Orders
• Doping the chiral spin liquid -- topological superconductor or chiral metal?
• Characterization of quantum spin liquids and their spinon band structures via functional renormalization
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
• Method to identify parent Hamiltonians for trial states
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Model Fractional Chern Insulators
• Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models
• A Kagome Map of Spin Liquids: from XXZ to Dzyaloshinskii-Moriya Ferromagnet
• Thermodynamics of Chiral Spin Liquids with Abelian and Non-Abelian Anyons
• Lattice spin models for non-Abelian Chiral Spin Liquids
• Competing Chiral Orders in the Topological Haldane-Hubbard Model of Spin-1/2 Fermions and Bosons
• Abelian SU$(N{)}_1$ Chiral Spin Liquids on the Square Lattice
• Bosonic Pfaffian State in the Hofstadter-Bose-Hubbard Model
• Spin structure factors of chiral quantum spin liquids on the kagome lattice
• Lattice effects on Laughlin wave functions and parent Hamiltonians
• Gapless chiral spin liquid from coupled chains on the kagome lattice
• Non-Abelian Chiral Spin Liquid on the Kagome Lattice
• Zero modes, Bosonization and Topological Quantum Order: The Laughlin State in Second Quantization
• Space group symmetry fractionalization in a chiral kagome Heisenberg antiferromagnet
• Algebraic approach to the study of zero modes of Haldane pseudopotentials
• Non-Abelian chiral spin liquid on a simple non-Archimedean lattice
• Coexistence of non-Abelian chiral spin liquid and magnetic order in a spin-1 antiferromagnet
• Nematic Spin Liquid Phase in a Frustrated Spin-1 System on the Square Lattice
• Deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator
• Parent Hamiltonian Reconstruction of Jastrow-Gutzwiller Wavefunctions
• Chiral spin liquid and quantum phase diagram of spin-$1/2$ $J_1$-$J_2$-$J_{\chi }$ model on the square lattice
• Continuum limit of lattice models with Laughlin-like ground states containing quasiholes
• Exact chiral spin liquid state in a Kitaev type spin model
• Majorana chiral spin liquid in Mott insulating cuprates
• On the origin of the possible chiral spin liquid state of the triangular lattice Hubbard model
• Lattice Laughlin states on the torus from conformal field theory
• Possible SU(3) Chiral Spin Liquid on the Kagome Lattice
• Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories
• Non-Abelian Fractional Chern Insulator in Disk Geometry
• Fermionic non-Abelian fractional Chern insulators from dipolar interactions
• Spin Correlations and Topological Entanglement Entropy in a Non-Abelian Spin-1 Spin Liquid
• Kitaev model on Hurwitz hyperbolic tilings: A non-Abelian gapped chiral spin liquid
• Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus
• Non-Abelian Statistics in one dimension: topological momentum spacings and SU(2) level $k$ fusion rules
• Exact Topological Flat Bands from Continuum Landau Levels
• Edge states for the Kalmeyer-Laughlin wave function
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Topologically-driven three-spin chiral exchange interactions treated from first principles
• Global quantum phase diagram and non-Abelian chiral spin liquid in a spin-3/2 square lattice antiferromagnet
• Fractional Spin Quantum Hall Effect in Weakly Coupled Spin Chain Arrays
• Efficient conversion from fermionic Gaussian states to matrix product states
• Conformal field theory and the non-abelian $SU(2{)}_k$ chiral spin liquid
• Quantum Thermal Hall effect of chiral spinons on a Kagome strip
• Non-Abelian chiral spin liquid on spin-1 kagome lattice: truncation of an exact Hamiltonian and numerical optimization
• Chiral spin liquid phase in an optical lattice at mean-field level
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• Flux-driven quantum spin liquids in kagome optical lattices
• Parent Hamiltonian Reconstruction via Inverse Quantum Annealing
• Chiral Bosonic Topological Insulator on the Honeycomb Lattice with Anisotropic Interactions