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.
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.
Recently, the frustrated XY model for spins 1/2 on the honeycomb lattice has attracted a lot of attention in relation with the possibility to realize a chiral spin liquid state. This model is relevant to the physics of some quantum magnets. Using the flexibility of ultracold atom setups, we propose an alternative way to realize this model through the Mott regime of the bosonic Kane-Mele-Hubbard model. The phase diagram of this model is derived using bosonic dynamical mean-field theory. Focusing on the Mott phase, we investigate its magnetic properties as a function of frustration. We do find an emergent chiral spin state in the intermediate frustration regime. Using exact diagonalization we study more closely the physics of the effective frustrated XY model and the properties of the chiral spin state. This gapped phase displays a chiral order, breaking time-reversal and parity symmetry, but is not topologically ordered (the Chern number is zero).
Motivated by experiments on ultracold atoms which have realized the Haldane model for a Chern insulator, we consider its strongly correlated Mott limit with spin-1/2 fermions. A slave rotor mean field theory suggests the appearance of gapped or gapless chiral spin liquid Mott insulators. To study competing magnetic orders, we consider the strong coupling effective spin Hamiltonian which includes chiral three-spin exchange. We obtain its classical phase diagram, uncovering various chiral magnetic orders including tetrahedral, cone, and noncoplanar spiral states which can compete with putative chiral quantum spin liquids. We study the effect of thermal fluctuations on these states, identifying crossovers in the spin chirality, and phase transitions associated with lattice symmetry breaking. We also discuss analogous effective spin Hamiltonians for correlated spin-1/2 bosons.
Spin liquids are novel states of matter with fractionalized excitations. A recent numerical study of Hubbard model on a honeycomb lattice\cite{Meng2010} indicates that a gapped spin liquid phase exists close to the Mott transition. Using Projective Symmetry Group, we classify all the possible spin liquid states by Schwinger fermion mean-field approach. We find there is only one fully gapped spin liquid candidate state: "Sublattice Pairing State" that can be realized up to the 3rd neighbor mean-field amplitudes, and is in the neighborhood of the Mott transition. We propose this state as the spin liquid phase discovered in the numerical work. To understand whether SPS can be realized in the Hubbard model, we study the mean-field phase diagram in the
J1−J2 spin-1/2 model and find an s-wave pairing state. We argue that s-wave pairing state is not a stable phase and the true ground state may be SPS. A scenario of a continuous phase transition from SPS to the semimetal phase is proposed. This work also provides guideline for future variational studies of Gutzwiller projected wavefunctions.
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.
Motivated by the recent numerical evidence [Z. Meng, T. Lang, S. Wessel, F. Assaad, and A. Muramatsu, Nature (London) 464, 847 (2010)] of a short-range resonating valence bond state in the honeycomb lattice Hubbard model, we consider Schwinger boson mean field theories of possible spin liquid states on honeycomb lattice. From general stability considerations the possible spin liquids will have gapped spinons coupled to
Z2 gauge field. We apply the projective symmetry group method to classify possible
Z2 spin liquid states within this formalism on honeycomb lattice. It is found that there are only two relevant
Z2 states, differed by the value of gauge flux, zero or $\ensuremath{\pi}$, in the elementary hexagon. The zero-flux state is a promising candidate for the observed spin liquid and continuous phase transition into commensurate N\'eel order. We also derive the critical field theory for this transition, which is the well-studied O(4) invariant theory [A. V. Chubukov, T. Senthil, and S. Sachdev, Phys. Rev. Lett. 72, 2089 (1994); A. V. Chubukov, S. Sachdev, and T. Senthil, Nucl. Phys. B 426, 601 (1994); S. V. Isakov, T. Senthil, and Y. B. Kim, Phys. Rev. B 72, 174417 (2005)], and has an irrelevant coupling between Higgs and boson fields with cubic power of spatial derivatives as required by lattice symmetry. This is in sharp contrast to the conventional theory [S. Sachdev and N. Read, Int. J. Mod. Phys. B 5, 219 (1991)], where such transition generically leads to incommensurate magnetic order. In this scenario the
Z2 spin liquid could be close to a tricritical point. Soft boson modes will exist at seven different wave vectors. This will show up as low-frequency dynamical spin susceptibility peaks not only at the $\ensuremath{\Gamma}$ point (the N\'eel order wave vector) but also at Brillouin-zone-edge center
M points and twelve other points. Some simple properties of the $\ensuremath{\pi}$-flux state are studied as well. Symmetry allowed further neighbor mean field ansatz are derived in appendices which can be used in future theoretical works along this direction.