Topological quantum phase transition in Kane-Mele-Kondo lattice model

We systematically explore the ground-state phase diagram of the Kane-Mele-Kondo lattice model on the honeycomb lattice; particularly, we focus on its magnetic properties, which are ubiquitous and important in many realistic heavy-fermion materials but have not been clearly studied in the previous publication [X. Y. Feng, J. Dai, C. H. Chung, and Q. Si, Phys. Rev. Lett. 111, 016402 (2013)]. Besides the Kondo insulator found in that paper, two kinds of antiferromagnetic spin-density-wave phases are discovered. One is the normal antiferromagnetic spin-density-wave state and the other is a nontrivial topological antiferromagnetic spin-density-wave state, which shows the unexpected Z(2) topological order with a quantized spin Hall conductance and a helical edge state similar to the hotly studied topological insulators. The quantum spin Hall insulator in the work of Feng et al. is found to be absent since it is always unstable to antiferromagnetic spin-density-wave states at least at the mean-field level in our model. Interestingly, the transition between the two spin-density-wave phases is an exotic topological quantum phase transition, whose critical behavior is described by an emergent three-dimensional quantum electrodynamics, in which conduction electrons contribute to the low-energy Dirac fermions while the spin-wave fluctuation of local spins gives rise to an effective dynamic U(1) gauge field. Such nontrivial transition shows radical critical thermodynamic, transport, and single-particle behaviors, which provide a fingerprint for this transition. Additionally, the transition of antiferromagnetic spin-density-wave states to the Kondo insulator is found to be first order. The introduction of two novel magnetic phases and their topological quantum phase transition show rich and intrinsic physics involved in the Kane-Mele-Kondo lattice model.