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Journal of Physics Conference Series

Phase diagrams of the Kane-Mele-Hubbard model in the presence of an external magnetic field

Ya‐Min Quan, Wei-Cheng Bao, Wei-Hua Wang, Dayong Liu

Published May 17, 2017• 1 citation
Publisher

Abstract

We studied the Kane-Mele-Hubbard model at half filling with Zeeman magnetic field using rotationally invariant slave boson method. The competition between external magnetic field and spin orbital coupling at large Hubbard U is explored. It is found that different canted antiferromagnetic phases exist in the presence of longitudinal and transverse magnetic fields. With longitudinal external magnetic field and strong electron correlation, the z component of the local moment is preferred by the finite spin-orbital coupling.

DOI
10.1088/1742-6596/827/1/012009

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We studied the Kane-Mele-Hubbard model at half filling with Zeeman magnetic field using rotationally invariant slave boson method. The competition between external magnetic field and spin orbital coupling at large Hubbard U is explored. It is found that different canted antiferromagnetic phases exist in the presence of longitudinal and transverse magnetic fields. With longitudinal external magnetic field and strong electron correlation, the z component of the local moment is preferred by the finite spin-orbital coupling.
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The phase diagram of the strongly correlated Hubbard model with intrinsic spin-orbit coupling on the honeycomb lattice is explored here. We obtain the low-energy effective model describing the spin degree of freedom. The resulting model is then studied by the Schwinger boson and Schwinger fermion approaches. The Schwinger boson method elucidates the boundary between the spin liquid phase and the magnetically ordered phases, Neel order, and incommensurate Neel order. Increasing the strength of the spin-orbit coupling is shown to narrow the width of the spin liquid region. The Schwinger fermion approach sheds further light on the nature of the spin liquid phase. We obtained three different candidates for the spin liquid phase within the mean-field approximation, namely, the gapless spin liquid, topological Mott insulator (fractionalized topological insulator), and chiral spin liquid phases. However, we argue that the gauge fluctuations and the instanton effect may suppress the first two spin liquids, while the chiral spin liquid is stable against gauge fluctuations due to its nontrivial topology.
By deriving a generalized Harper's equation, we investigate the effects of temperature TTT and hole doping $\d$ on antiferromagnetically correlated electrons under the influence of an applied magnetic field. We obtain a phase diagram in a TTT-$\d$ plane for staggered magnetization under the external field. We find that away from half filling the maximum values of staggered magnetization occur with rapid convergence to a finite temperature constant near half filling. We discover the reentrant behavior of the staggered magnetization in the presence of the magnetic field.
Magnetic properties of Hubbard model have been studied extensively. A theoretical description of these states, however, is not straight forward within conventional mean-field approach due to the electron correlation effects. Here we provide a slave spin theory of the magnetic states in the single band Hubbard model. By introducing an additional decomposition of the on-site Coulomb interaction in the magnetic channel in both the slave spin and the fermionic spinon sectors, we show a magnetic solution with renormalized quasiparticle spectral weight can be stabilized at both half-filling and finite doping. By comparing the energies of antiferromagnetic and ferromagnetic states, we provide a ground-state phase diagram for generic electron filling. We further discuss possible generalization of the slave-spin method.
We investigate how the in-plane Zeeman field and the Hubbard interaction can jointly affect the topological states in the Kane-Mele-Hubbard model. At low Zeeman field, the projector quantum Monte Carlo (PQMC) simulations demonstrate Mott transitions between the higher-order topological insulator induced by the in-plane Zeeman field and the antiferromagnetic insulator induced by the Hubbard interaction. The interacting higher-order topological state on a finite-sized honeycomb lattice is characterized by the local density of states derived from the real-space spectral function. In the higher-order topological phase, the mirror-symmetry protected corner states exist on the diamond-shaped honeycomb lattice. In terms of spatial extent of corner states induced by the in-plane Zeeman field in the Kane-Mele and Kane-Mele-Hubbard models, we show that the effect of the Hubbard interaction is to contribute some extra in-plane Zeeman field. At the mean-field level, we characterize the bulk topology by the mirror winding number and calculate the full phase diagram of the Kane-Mele-Hubbard model under the influence of the in-plane Zeeman field. The mean-field phase diagram shows that a high in-plane Zeeman field drives the system into a spin-polarized (topologically trivial) phase. In particular, the upper limit of the Zeeman field that can induce corner states in the Kane-Mele model is found to be hc=1.0{h}_{c}=1.0hc​=1.0. In the parameter region of PQMC simulations, the mean-field solutions qualitatively agree with the PQMC results.
We study a spin-1 ultracold Bose gas in the presence of both external and synthetic magnetic fields via mean-field approach corresponding to both signs of the spin-dependent interaction potential. The synthetic field is included through the hopping frequencies via Peierls coupling and the external field through the Zeeman interaction term to explore the influence of one over the other. The antiferromagnetic case shows that at low values of external field strengths, the spin singlet state is stable and the system is more likely in Mott insulating (MI) phase as the synthetic field is enhanced. But at large external fields, due to a competition between the hopping and the Zeeman interaction terms, the former tends to stabilize the MI phase compared to the superfluid (SF) phase, while the latter tries to destabilize the MI phase by suppressing the formation of singlet pairs. In the ferromagnetic case, insensitivity of the phase properties to the external magnetic field leads to stabilization of the MI phase with increasing synthetic magnetic field. Further the magnetization shows that there are distinct signatures of transverse polar and longitudinal ferro SF phases for both antiferromagnetic and ferromagnetic interactions, respectively.