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.

中文翻译：

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共形场论和非阿贝尔SU(2)k手性自旋液体

我们构建了一系列一维和二维长程 SU(2) 自旋模型作为与无限维矩阵乘积状态相关的父哈密顿量，这些状态由 $SU(2)_k$ WZW 模型中的简单当前相关函数产生。我们的结果为 Greiter 及其合著者最近关于实现非阿贝尔手性自旋液体的提议提供了共形场理论基础。我们特别解释了参考文献中建议的基态波函数幅度的对称化过程。arXiv:0903.4547 源自共形场论描述。