Kondo spin liquid in the Kondo necklace model: Classical disordered phase versus symmetry-protected topological state

Abstract

We study possible topological features of Kondo spin liquid phase in terms of the one-and twodimensional Kondo necklace models within the frame work of quantum O(N) non-liner sigma model (NLSM). In the one-dimensional case, it is found that the bulk properties of the Kodno spin liquid phase are similar to the well-known Haldane phase at strong coupling fixed point. The difference between them mainly comes from their boundaries due to the effect of the topological term. In the two-dimensional case, the system can be mapped onto an O(4)-like NLSM with some O(3) anisotropy. Interestingly, we find that if hedgehog-like point defects are included together with the restoration of the full O(4) symmetry, our model is identical to a kind of SU(2) symmetryprotected topological (SPT) state. Additionally, if the system has the O(5) symmetry instead, the effective NLSM with Wess-Zumino-Witten term is just a description of the surface modes of a threedimensional SPT state, though such O(5) NLSM could not be a proper description of Kondo spin liquid phase due to its gaplessness. We expect that the discussions might provide useful threads to identify certain microscopic bilayer antiferromagnet models (and related materials), which can support the desirable SPT states.

Topological phase in 1D topological Kondo insulator: Z2 topological insulator, Haldane-like phase and Kondo breakdown

“…The J-term denotes the p-wave-like 'Kondo' coupling and it has staggered features, which may lead to effective ferromagnetic coupling between these two chains and we expect a Haldane-like phase can form in this model. [42] However, we should remind the reader that the Kondo necklace model cannot be derived from the original Kondo lattice model at half-filling but can only be considered as a phenomenological model devised for studying the low-lying spin excitations.…”

Mesenchymal stem cell response to UV-photofunctionalized TiO2coated CoCrMo

“…1 Furthermore, revision surgery is set to follow this trend, placing increased pressure on the industry, both clinically and economically. 2,3 To cope with this anticipated situation, improving current generation biomaterials is a high priority and can be achieved by methods such as surface modication. We have previously shown that coating cobaltchromium-molybdenum (CoCrMo) in a layer of anatase TiO 2 by APCVD, can improve the osteogenic differentiation and adhesion of human mesenchymal stem cells (MSCs) in vitro.…”