Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
arXiv:2501.09567 · doi:10.1103/PhysRevB.111.205137
Abstract
We employ the Wess-Zumino-Witten (WZW) model in conformal field theory to construct lattice wave functions in both one and two dimensions. The spins on all lattice sites are chosen to transform under the irreducible representation with a single row and boxes in the Young tableau. It is demonstrated that the wave functions can be reinterpreted as parton states, which enables efficient conversion to matrix product states such that many physical properties can be evaluated directly. In one dimension, these wave functions describe critical spin chains whose universality classes are in one-to-one correspondence with the WZW models used in the construction. In two dimensions, our constructions yield model wave functions for chiral spin liquids, and we show how to find all topological sectors of them in a systematic way. Using the null vectors of Kac-Moody algebras, parent Hamiltonians of the series are derived. The chiral spin liquids are lattice analogs of non-Abelian spin-singlet fractional quantum Hall states, and the member hosts Fibonacci anyons.
15 pages, 6 figures
References in corpus (31)
- 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
- Non-Abelian Statistics in a Quantum Antiferromagnet
- 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
- Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
- Abelian SU Chiral Spin Liquids on the Square Lattice
- Finite and Infinite Matrix Product States for Gutzwiller Projected Mean-Field Wavefunctions
- Anyon braiding in semi-analytical fractional quantum Hall lattice models
- Infinite Matrix Product States for long range SU(N) spin models
- Universal entropy of conformal critical theories on a Klein bottle
- Realization of higher Wess-Zumino-Witten models in spin chains
- Matrix product states for Hartree-Fock-Bogoliubov wave functions
- Universal Boundary Entropies in Conformal Field Theory: A Quantum Monte Carlo Study
- A model of chiral spin liquids with Abelian and non-Abelian topological phases
- Real-space entanglement spectra of parton states in fractional quantum Hall systems
- Coexistence of non-Abelian chiral spin liquid and magnetic order in a spin-1 antiferromagnet
- Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice
- From SU(2) to SU(2) Wess-Zumino-Witten transitions in a frustrated spin-5/2 chain
- Universal scaling of Klein bottle entropy near conformal critical points
- Truncation of lattice fractional quantum Hall Hamiltonians derived from conformal field theory
- Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories
- Extracting the Luttinger parameter from a single wave function
- Network construction of non-Abelian chiral spin liquids
- 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
- Conformal field theory approach to parton fractional quantum Hall trial wave functions
- Realization of Wess-Zumino-Witten transitions with levels and in a frustrated spin-3 chain
- Efficient conversion from fermionic Gaussian states to matrix product states
- Non-Abelian chiral spin liquid on spin-1 kagome lattice: truncation of an exact Hamiltonian and numerical optimization
- Constructive Fermionic Matrix Product States for Projected Fermi Sea