We study the two-dimensional Kane-Mele-Hubbard model at half filling by means of quantum Monte Carlo simulations. We present a refined phase boundary for the quantum spin liquid. The topological insulator at finite Hubbard interaction strength is adiabatically connected to the groundstate of the Kane-Mele model. In the presence of spin-orbit coupling, magnetic order at large Hubbard $U$ is restricted to the transverse direction. The transition from the topological band insulator to the antiferromagnetic Mott insulator is in the universality class of the three-dimensional XY model. The numerical data suggest that the spin liquid to topological insulator and spin liquid to Mott insulator transitions are both continuous.We study the two-dimensional Kane-Mele-Hubbard model at half filling by means of quantum Monte Carlo simulations. We present a refined phase boundary for the quantum spin liquid. The topological insulator at finite Hubbard interaction strength is adiabatically connected to the groundstate of the Kane-Mele model. In the presence of spin-orbit coupling, magnetic order at large Hubbard $U$ is restricted to the transverse direction. The transition from the topological band insulator to the antiferromagnetic Mott insulator is in the universality class of the three-dimensional XY model. The numerical data suggest that the spin liquid to topological insulator and spin liquid to Mott insulator transitions are both continuous.

arXiv:1111.3949Physical Review BMar 29, 2012159 citations

Quantum Phase Transition in the Infinite Dimensional Hubbard Model

Yasuo Y. Suzuki, Shin-ichi Saito, Susumu Kurihara

Journal of Low Temperature PhysicsDec 1, 19980 citations

Phase transitions of the dimerized Kane–Mele model with/without strong interaction

Tao Du, Yue-Xun Li, Yan Li +2 more

The dimerized Kane-Mele model with/without strong interaction is studied using analytical methods. The boundary of the topological phase transition of the model without strong interaction is obtained. Our results show that the occurrence of the transition only depends on dimerized parameter [Formula: see text]. From the one-particle spectrum, we obtain the completed phase diagram including the quantum spin Hall state and the topologically trivial insulator. Then, using different mean field methods, we investigate the Mott transition and the magnetic transition of the strongly correlated dimerized Kane-Mele model. In the region between the two transitions, the topological Mott insulator with characteristics of Mott insulators and topological phases may be the most interesting phase. In this work, the effects of hopping anisotropy and Hubbard interaction U on the boundaries of the two transitions are observed in detail. The completed phase diagram of the dimerized Kane-Mele-Hubbard model is also obtained in this work. Quantum fluctuations have extremely important influences on a quantum system. However, investigations are under the framework of mean field treatment in this work and the effects of fluctuations in this model will be discussed in the future.The dimerized Kane-Mele model with/without strong interaction is studied using analytical methods. The boundary of the topological phase transition of the model without strong interaction is obtained. Our results show that the occurrence of the transition only depends on dimerized parameter [Formula: see text]. From the one-particle spectrum, we obtain the completed phase diagram including the quantum spin Hall state and the topologically trivial insulator. Then, using different mean field methods, we investigate the Mott transition and the magnetic transition of the strongly correlated dimerized Kane-Mele model. In the region between the two transitions, the topological Mott insulator with characteristics of Mott insulators and topological phases may be the most interesting phase. In this work, the effects of hopping anisotropy and Hubbard interaction U on the boundaries of the two transitions are observed in detail. The completed phase diagram of the dimerized Kane-Mele-Hubbard model is also obtained in this work. Quantum fluctuations have extremely important influences on a quantum system. However, investigations are under the framework of mean field treatment in this work and the effects of fluctuations in this model will be discussed in the future.

arXiv:1708.09235Journal of Physics Condensed MatterJun 20, 20170 citations

U

is restricted to the transverse direction. The transition from the topological band insulator to the antiferromagnetic Mott insulator is in the universality class of the three-dimensional XY model. The numerical data suggest that the spin liquid to topological insulator and spin liquid to Mott insulator transitions are both continuous.