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

TL;DR

This paper introduces a novel spin-1 lattice wave function that realizes a non-Abelian chiral spin liquid with topological order, inspired by fractional quantum Hall states, using conformal field theory techniques.

Contribution

It constructs resonating valence bond wave functions for spin-1 systems on a torus that exhibit non-Abelian topological order, linking lattice models to conformal field theory.

Findings

Explicit three-fold degenerate ground states

Analytical modular S and T matrices

Lattice analogues of Moore-Read state

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.