Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus

Abstract

We propose resonating valence bond wave functions for a spin-1 system on the torus that realize a non-Abelian chiral spin liquid. The wave functions take the form of infinite dimensional matrix product states constructed from conformal blocks of the $\mathrm{SO}(3{)}_1$ Wess-Zumino-Witten model. This means that they are lattice analogues of the bosonic Moore-Read state introduced in fractional quantum Hall systems. The topological order of this system is revealed by explicit construction of three-fold degenerate ground states and analytical computation of the modular S and T matrices.

arXiv comment11 pages, 2 figures

References in corpus (37)

• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Quantum Spin Liquid States
• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Quantum Hall Physics - hierarchies and CFT techniques
• Infinite matrix product states, Conformal Field Theory and the Haldane-Shastry model
• Projective Construction of Non-Abelian Quantum Hall Liquids
• Non-Abelian Statistics in a Quantum Antiferromagnet
• The Ground State Structure and Modular Transformations of Fractional Quantum Hall States on a Torus
• Fermionic magnons, non-Abelian spinons, and spin quantum Hall effect from an exactly solvable Kitaev Hamiltonian with SU(2) symmetry
• Microscopic models for Kitaev's sixteenfold way of anyon theories
• Laughlin spin liquid states on lattices obtained from conformal field theory
• Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
• Parent Hamiltonian for the non-Abelian chiral spin liquid
• Quantum spin Hamiltonians for the SU(2)_k WZW model
• Paired chiral spin liquid with a Fermi surface in S=1 model on the triangular lattice
• Lattice Laughlin States of Bosons and Fermions at Filling Fractions $1/q$
• Exotic S=1 spin liquid state with fermionic excitations on triangular lattice
• 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
• Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models
• Fermionic theory for quantum antiferromagnets with spin S > 1/2
• Lattice spin models for non-Abelian Chiral Spin Liquids
• Possibility of S=1 spin liquids with fermionic spinons on triangular lattices
• Infinite Matrix Product States for long range SU(N) spin models
• Gutzwiller Projected wavefunctions in the fermonic theory of S=1 spin chains
• Non-Abelian Chiral Spin Liquid on the Kagome Lattice
• 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
• Lattice Laughlin states on the torus from conformal field theory
• Spin Correlations and Topological Entanglement Entropy in a Non-Abelian Spin-1 Spin Liquid
• Superconductivity, pair density wave, and Neel order in cuprates
• Conformal field theory and the non-abelian $SU(2{)}_k$ chiral spin liquid

Cited by in corpus (8)

• Ising-like and Fibonacci-Anyons from KZ-equations
• Chiral conformal field theory for topological states and the anyon eigenbasis on the torus
• Restricted Boltzmann machine representation for the groundstate and excited states of Kitaev Honeycomb model
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Non-Abelian chiral spin liquid on spin-1 kagome lattice: truncation of an exact Hamiltonian and numerical optimization
• Efficient conversion from fermionic Gaussian states to matrix product states
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• Non-Abelian topological order with SO(5)${}_1$ chiral edge states