"Spin liquids" are elusive quantum states of matter, characterized by topological order and a spectrum of fractionalized excitations rather than by broken symmetries. As the study of spin-liquids is still in a formative stage, it is useful to construct exactly solvable model problems with various flavors of spin liquid ground states, so as to establish their stability as phases of matter and to derive essential features of their physical properties crisply. Here we study two such models: Firstly, we show that two distinct chiral spin liquid phases are realized in a spin-1/2 Kitaev model on a decorated honeycomb lattice. Depending on coupling parameters, its vortex excitations (visons) obey Abelian or non-Abelian statistics. The quantum phase transition between the two phases is continuous, although purely topological. Secondly, we introduce a spin-3/2 model on the square lattice, which is related to a model introduced previously by Wen. This model has a half integer spin per unit cell, and an algebraic spin liquid ground state. Remarkably, although the model can be written entirely in terms of bare bosonic operators, by fine-tuning a single parameter in the model, fermionic excitations with an emergent Fermi surface can be realized.
Reference: 1. Hong Yao and Steven A. Kivelson, Phys. Rev. Lett. 99, 247203 (2007)
Reference: 2. Hong Yao, Shou-Cheng Zhang and Steven A. Kivelson, arXiv: 0810.5347.