Yin Zhong, Yu-Feng Wang, Hong-Gang Luo
In this paper, we study possible topological features of Kondo spin liquid phase in the one and two-dimensional Kondo necklace models. In terms of quantum O(3) non-liner sigma model (NLSM) field theory supported with topological $\theta$ terms, it is found that in the one-dimensional case the Kodno spin liquid phase and the well-known Haldane phase have similar bulk properties described by NLSM without topological term at strong coupling fixed point and their topological terms give trivial contribution in closed manifold. The difference between these two phases mainly originates from their boundary. Explicitly, the Haldane phase has fractionalized S=1/2 spins while the Kodno spin liquid does not support such degree of freedom on either side of the open chains. Thus we may consider the Kondo spin liquid in Kondo necklace model as a classical disordered phase although it is indeed a quantum paramagnetic phase. In addition, we also analyze the topological properties of Kondo spin liquid in high dimensional Kondo necklace models by an O(4)-like NLSM with O(3) anisotropy. If a hedgehog-like topological defect is ignored, it seems that the existence of topologically non-trivial Kondo spin liquid might have to include spin-orbit coupling-like element. More interestingly, when hedgehogs are included with the full O(4) symmetry, our model is identical to a kind of SU(2) symmetry-protected topological (SPT) states. This indicates that certain microscopic two-layer antiferromagnet models could support the desirable SPT states and suggests that even some real-world two-layer materials might be devised in near future.
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http://arxiv.org/abs/1305.2575
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