某些高维量子自旋模型的费米化变换
Fermionization Transform for Certain Higher-Dimensional Quantum Spin Models
摘要：
提出了一种推广的Jordan-Wigner变换，它允许精确地费米子化一个大家族的量子自旋哈密顿量在维度高于一。关键的新步骤是通过向原始模型添加一组独立的自由自旋来扩大原始模型的希尔伯特空间，并使用这些辅助算子和晶格自旋的组合来构建物理哈密顿量的适当费米子表示。该变换对于晶格自旋哈密顿量特别有用，其中XY型的双自旋相互作用不存在或仅存在于一维链中，并且其中链通过伊辛型的双自旋相互作用、环交换项或更一般的多自旋相互作用耦合，所述多自旋相互作用涉及来自每个链的偶数个自旋算子。使用所提出的费米子化方法，我们提供了一个简单的参数，表明与Paramekanti，Balents和Fisher [Phys. Rev. B 66，054526（2002）]提出的环交换模型密切相关的自旋哈密顿量确实实现了自旋液体状态。
英文摘要：
Proposed is a generalization of Jordan-Wigner transform that allows to exactly fermionize a large family of quantum spin Hamiltonians in dimensions higher than one. The key new steps are to enlarge the Hilbert space of the original model by adding to it a collection of stand-alone free spins and to use a combination of these auxiliary operators and the lattice spins to construct a proper fermion representation of the physical Hamiltonian. The transform is especially useful for lattice spin Hamiltonians, where two-spin interactions of XY-type are either absent or exist only within one-dimensional chains and where the chains are coupled via two-spin interactions of Ising type, ring-exchange terms, or more general multi-spin interactions that involve an even number of spin operators from each chain. Using the proposed fermionization method we provide a simple argument suggesting that a spin Hamiltonian closely-related to the ring-exchange model proposed by Paramekanti, Balents, and Fisher [Phys. Rev. B 66, 054526 (2002)] indeed realizes a spin-liquid state.
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