A non-abelian spin liquid in triangular lattice spin-1 systems was recently formulated in the form of continuum field theory [T. Grover, and T. Senthil, Phys. Rev. Lett. 107, 077203 (2011); Cenke Xu, A.W.W. Ludwig, arXiv:1012.5671]. It has spin-1/2 bosonic spinons coupled to emergent quaternion gauge fields, and can be obtained by quantum disordering a non-collinear spin nematic order hypothesized to describe NiGa_2S_4 [H. Tsunetsugu, and M. Arikawa, J. Phys. Soc. Jpn. 75, 083701 (2006)], However a microscopic lattice description, e.g. the lattice spinon (mean-field) Hamiltonian and the spin wavefunction, has been missing, and it has been noted that the standard Schwinger boson or bosonic triplon representations of spin-1 cannot describe this spin liquid. In this paper a two-orbital Schwinger boson representation for spin-1 systems is developed and used to construct a mean-field description of this quaternion spin liquid. Projecting the mean-field state produces a prototype wavefunction, which is a superposition of close-packed AKLT loop configurations with nontrivial amplitudes. This new formalism and related wavefunctions may be generalized to higher spin systems and can possibly produce spin liquid states with even richer emergent gauge structures.
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.
We study possible spin liquids on square lattice that respect all lattice symmetries and time-reversal symmetry within the framework of Schwinger boson (mean-field) theory. Such spin liquids have spin gap and emergent
Z2 gauge field excitations. We classify them by the projective symmetry group method, and find six spin-liquid states that are potentially relevant to the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model. The properties of these states are studied under mean-field approximation. Interestingly we find a spin-liquid state that can go through continuous phase transitions to either the N\'eel magnetic order or magnetic orders of the wave vector at the Brillouin zone edge center. We also discuss the connection between our results and the Abrikosov fermion spin liquids.
Recent numerical simulations find a possible chiral spin-liquid state in the intermediate coupling regime of the triangular lattice Hubbard model. Here we provide a simple picture for its origin in terms of a bosonic resonating valence bond (RVB) description. More specifically, we show that such a chiral spin-liquid state can be understood as a quantum disordered tetrahedral spin state stabilized by the four spin ring exchange coupling, which suppresses the order-by-disorder effect toward a stripy spin state. Such a chiral spin-liquid state features a spin Berry phase of $\frac{\ensuremath{\pi}}{2}$ per triangle. However, we show that the topological property of such a state is totally missed in the Schwinger boson mean-field description as a result of the lack of boson rigidity caused by the no double occupancy constraint.
The Kitaev model is an exactly solvable model that exhibits a quantum spin liquid as its ground state. While this model was originally proposed as an S = 1 / 2 spin model on a honeycomb lattice, extensions to higher-spin systems have recently attracted attention. In contrast to the S = 1 / 2 case, such higher- S models are not exactly solvable and remain poorly understood, particularly for spin excitations at finite temperatures. Here, we focus on the S = 1 Kitaev model, which has been proposed to host bosonic quasiparticles. We investigate this model using Schwinger boson mean-field theory, where bosonic spinons are introduced as fractional quasiparticles by extending bond operators to address anisotropic spin interactions. We determine the mean-field parameters that realize a quantum spin liquid in both ferromagnetic and antiferromagnetic Kitaev models. Based on this mean-field ansatz, we calculate the dynamical and equal-time spin structure factors. We find that, when one uses the conventional decoupling scheme based on Wick decoupling with respect to spinons to calculate spin correlations, the resultant spin structure factors exhibit a momentum dependence that is not consistent with the sign structure expected from the exchange interaction: They possess a strong spectral weight indicating ferromagnetic (antiferromagnetic) correlations in the antiferromagnetic (ferromagnetic) Kitaev model. To resolve this issue, we propose an alternative scheme for evaluating the spin correlations, which is based on decoupling with respect to the bond operators. We demonstrate that, in our scheme, this discrepancy is removed, and the momentum dependence of the spin structure factors is consistent with the sign of the exchange constant. We also calculate the temperature evolution of the dynamical spin structure factor and find that the continuum observed at zero temperature splits into two distinct structures as the temperature increases, which can be understood in terms of the bandwidth narrowing of spinons. Finally, we clarify the origin of why the two distinct decoupling schemes result in different momentum dependences of the spin structure factors and discuss their relationship to results obtained in previous studies.
We find that the Schwinger boson mean field theory (SBMFT) supplemented with Gutzwiller projection provides an exceedingly accurate description for the ground state of the spin-12triangular lattice antiferromagnetic Heisenberg model (spin-12TLHAF). However, we find the SBMFT fails even qualitatively in the description of the dynamical behavior of the system. In particular, the SBMFT fails to predict the Goldstone mode in the magnetic ordered phase. We show that the coherent peak in the two-spinon continuum in the presence of spinon condensate should not be interpreted as a magnon mode. The SBMFT also predicts incorrectly a gapless longitudinal spin fluctuation mode in the magnetic ordered phase. We show that these failures are related to the following facts: (1) spinon condensation fails to provide a consistent description of the order parameter manifold of the 120 degree ordered phase. (2) There lacks in the SBMFT the coupling between the uncondensed spinon and the spinon condensate, which breaks both the spin rotational and the translational symmetry. (3) There lacks in the SBMFT the rigidity that is related to the no double occupancy constraint on the spinon system. We show that such failures of the SBMFT is neither restricted to the spin-12TLHAF nor to the magnetic ordered phase. We proposed a generalized SBMFT to resolve the first two issues and a new formalism to address the third issue.