Lattice spin models for non-Abelian Chiral Spin Liquids

Abstract

We suggest a class of two-dimensional lattice spin Hamiltonians describing non-Abelian SU(2) chiral spin liquids - spin-analogues of fractional non-Abelian quantum Hall states- with gapped bulk and gapless chiral edge excitations described by the SU(2)${}_n$ Wess-Zumino-Novikov-Witten conformal field theory. The models are constructed from an array of a generalized spin-$n/2$ ladders with multi-spin exchange interaction which are coupled by isolated spins. Such models allow a controllable analytic treatment starting from the one-dimensional limit and are characterized by a bulk gap and non-Abelian SU(2)${}_n$ gapless edge excitations.

7 pages, one figure, replaced by an updated version

References in corpus (9)

• An exact chiral spin liquid with non-Abelian anyons
• Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagomé Lattice
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Ordering in spatially anisotropic triangular antiferromagnets
• Chiral Spin Liquid and Quantum Criticality in Extended $S=1/2$ Heisenberg Models on the Triangular Lattice
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Chiral Spin Liquids in Arrays of Spin Chains
• Spatially Anisotropic Heisenberg Kagome Antiferromagnet
• Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states

Cited by in corpus (33)

• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
• Extension of the standard Heisenberg Hamiltonian to multispin exchange interactions
• Emergence of Chiral Spin Liquids via Quantum Melting of Non-Coplanar Magnetic Orders
• Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
• Coupled-wire constructions: a Luttinger liquid approach to topology
• DMRG simulations of SU(N) Heisenberg chains using standard Young tableaux: fundamental representation and comparison with finite-size Bethe ansatz
• Gapless chiral spin liquid from coupled chains on the kagome lattice
• Non-Abelian chiral spin liquid on a simple non-Archimedean lattice
• Spin chain network construction of chiral spin liquids
• Dimensional crossover in the SU(4) Heisenberg model in the six-dimensional antisymmetric self-conjugate representation revealed by quantum Monte Carlo and linear flavor-wave theory
• Exact diagonalization of $\mathrm{SU}(N)$ Heisenberg and AKLT chains using the full $\mathrm{SU}(N)$ symmetry
• Chiral Spin Order in Kondo-Heisenberg systems
• From coupled wires to coupled layers: Model with three-dimensional fractional excitations
• Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions
• Exact chiral spin liquid state in a Kitaev type spin model
• Quantum criticality on a chiral ladder: an $SU(2)$ iDMRG study
• Network construction of non-Abelian chiral spin liquids
• 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
• Microscopic Study of the Coupled-Wire Construction and Plausible Realization in Spin-Dependent Optical Lattices
• Model of spin liquids with and without time-reversal symmetry
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Efficient conversion from fermionic Gaussian states to matrix product states
• Fractional Spin Quantum Hall Effect in Weakly Coupled Spin Chain Arrays
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Conformal field theory and the non-abelian $SU(2{)}_k$ chiral spin liquid
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• Majorana Fermi surface state in a network of quantum spin chains
• Non-Abelian topological order with SO(5)${}_1$ chiral edge states
• Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays
• Triangular lattice models of the Kalmeyer-Laughlin spin liquid from coupled wires
• Quantized edge magnetizations and their symmetry protection in one-dimensional quantum spin systems