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.

11 pages, 2 figures

References in corpus (7)

• Non-Abelian Anyons and Topological Quantum Computation
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Paired chiral spin liquid with a Fermi surface in S=1 model on the 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
• Fermionic theory for quantum antiferromagnets with spin S > 1/2
• Infinite Matrix Product States for long range SU(N) spin models

Cited by in corpus (7)

• Ising-like and Fibonacci-Anyons from KZ-equations
• Chiral conformal field theory for topological states and the anyon eigenbasis on the torus
• 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
• Non-Abelian chiral spin liquid on spin-1 kagome lattice: truncation of an exact Hamiltonian and numerical optimization
• 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