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The famous Kitaev model on the honeycomb lattice[1] is an exactly solvable yet experimentally realistic model of a quantum spin liquid. While strong evidences of this exotic state of matter have been reported, debate on the nature of the observed state persists. One of the reasons is due to the coexistence of other types of interactions in realistic materials, which raises the question about the fate of the Kitaev spin liquid under this context. In this talk, I’ll introduce two theoretical approaches that provide valuable insights to this issue. (I) Effective Hamiltonian approach[2,3]. We introduce an extension of the Kitaev honeycomb model by including four-spin interactions that preserve the local gauge structure and, hence, the integrability of the original model. The extended model has a rich phase diagram containing five distinct vison crystals, as well as a symmetric π-flux spin liquid with a Fermi surface of Majorana fermions and a sequence of Lifshitz transitions. It realizes more than half of the topological orders in Kitaev’s sixteen-fold way. We argue that our extended model emerges naturally from generic perturbations to the Kitaev honeycomb model. (II) Variational approach[4]. This approach reveals the physical origin of the asymmetry in the stability range of Kitaev spin liquid phases around the ferromagnetic and antiferromagnetic Kitaev limit. The same analysis reveals the emergence of bound states of fractionalized excitations in the proximity of the quantum phase transition between the Kitaev spin liquid and different magnetically ordered states. They will appear as sharp modes in the dynamical spin structure factor that is accessible through inelastic neutron scattering technique. Moreover, the type of magnetic ordering that is inferred from the dominant magnetic susceptibility coincides with the orderings that have been reported in different numerical works[5].
[1] Alexei Kitaev, “Anyons in an exactly solved model and beyond”, Annals of Physics 321 (2006) 2–111.
[2] Shang-Shun Zhang, Zhentao Wang, Gábor B. Halász, and Cristian D. Batista, “Vison Crystals in an Extended Kitaev Model on the Honeycomb Lattice”, Phys. Rev. Lett. 123, 057201 (2019).
[3] Shang-Shun Zhang, Cristian D. Batista, and Gábor B. Halász, “Toward Kitaev’s sixteenfold way in a honeycomb lattice model ”, Phys. Rev. Research 2, 023334 (2020).
[4] Shang-Shun Zhang, Gábor B. Halász, Wei Zhu, and Cristian D. Batista, “Variational study of the Kitaev-Heisenberg-Gamma model”, to be appeared soon.
[5] Jeffrey G. Rau, Eric Kin-Ho Lee, and Hae-Young Kee, “Generic Spin Model for the Honeycomb Iridates beyond the Kitaev Limit”, Phys. Rev. Lett. 112, 077204 (2014).
Dr. Zhang graduated from University of Science and Technology of China in 2011 and received my PhD at Institute of Physics, Beijing in 2016. He is currently a postdoctoral research associate at University of Minnesota, United States. His research interest mainly focuses on the frustrated magnetism, including the quantum spin liquid, anomalous magnetic excitations revealed by various experimental techniques, topological magnetic materials. He's also interested in the interplay between the superconductivity and the non-Fermi liquid.