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

TL;DR

This paper constructs 1D and 2D long-range SU(2) spin models based on conformal field theory, providing a theoretical foundation for non-abelian chiral spin liquids and explaining their ground state wave function symmetrization.

Contribution

It introduces a conformal field theory framework for non-abelian chiral spin liquids using $SU(2)_k$ WZW models and connects it to recent proposals on their realization.

Findings

Constructed parent Hamiltonians from CFT correlation functions.

Linked symmetrization of ground state wave functions to CFT descriptions.

Provided a theoretical basis for non-abelian chiral spin liquids.

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.