Conformal field theory and the non-abelian $SU(2{)}_k$ chiral spin liquid

Abstract

We construct a family of 1D and 2D long-range SU(2) spin models as parent Hamiltonians associated with infinite dimensional matrix product states that arise from simple current correlation functions in $SU(2{)}_k$ WZW models. Our results provide a conformal field theory foundation for recent proposals by Greiter and coauthors regarding the realization of non-abelian chiral spin liquids. We explain, in particular, how the symmetrization procedure for the amplitudes of the ground state wave function suggested in Ref. arXiv:0903.4547 originates from the conformal field theory description.

arXiv comment15 pages, 1 figure

References in corpus (28)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Infinite matrix product states, Conformal Field Theory and the Haldane-Shastry model
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Coupled wire construction of chiral spin liquids
• Parent Hamiltonian for the non-Abelian chiral spin liquid
• Chiral Spin Liquids in Arrays of Spin Chains
• Parent Hamiltonian for the Chiral Spin Liquid
• Quantum spin Hamiltonians for the SU(2)_k WZW model
• Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
• Antiferromagnetic spin-S chains with exactly dimerized ground states
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Projected BCS states and spin Hamiltonians for the SO(n)_1 Wess-Zumino-Witten model
• A family of spin-S chain representations of SU(2)_k Wess-Zumino-Witten models
• Lattice spin models for non-Abelian Chiral Spin Liquids
• Fractional spin liquid hierarchy for spin S antiferromagnets
• Infinite Matrix Product States for long range SU(N) spin models
• Realization of higher Wess-Zumino-Witten models in spin chains
• Lattice effects on Laughlin wave functions and parent Hamiltonians
• Mapping of Parent Hamiltonians: from Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains
• Infinite matrix product states, boundary conformal field theory, and the open Haldane-Shastry model
• Bosonic fractional quantum Hall states on the torus from conformal field theory
• Integrable open spin chains related to infinite matrix product states
• Lattice Laughlin states on the torus from conformal field theory
• Non-Abelian Statistics in one dimension: topological momentum spacings and SU(2) level $k$ fusion rules
• Spin-s wavefunctions with algebraic order
• Chain and ladder models with two-body interactions and analytical ground states

Cited by in corpus (4)

• 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
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders