A generalized Schwinger boson representation is proposed to describe the two-dimensional SU(4) symmetric spin-orbital quantum antiferromagnet. A uniform mean field solution gives rise to an antiferromagnetic long range ordered state with a small staggered magnetization
ms=0.07566, and the recent quantum Monte Carlo simulations on rather large lattice sizes have provided strong evidence to support these mean field results.
A generalized one-dimensional $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ spin-orbital model is studied by means of Schwinger boson mean-field theory (SBMFT). We focus on exploring the dimer phases and clarify how to capture properly the low-temperature properties of the system. The phase diagrams for the cases of
S=T=1∕2 and of
S=1 and
T=1∕2 are presented. Three dimer phases, the orbital valence bond state, spin valence bond state and spin-orbital valence bond state, are found to arise in proper parameter regions. The results indicate that the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ type of spin-orbit coupling can serve as both the spin-Peierls and orbital-Peierls mechanisms which are responsible for the formations of spin singlet and orbital singlet, respectively. We have also calculated the static spin and pseudospin susceptibilities in the SBMFT scheme to characterize and distinguish the three types of dimer phases.
A spin-
21 system with double orbital degeneracy may possess SU(4) symmetry. According to the group theory a global SU(4) singlet state can be expressed as a linear combination of all possible configurations consisting of four-site SU(4) singlets. Following Andersion's idea for spin-
21 system, we propose that the ground state for the antiferromagnetic SU(4) model is an SU(4)-resonating valence-bond (RVB) state. A short-range SU(4)-RVB state is a spin and orbital liquid, and its elementary excitations has an energy gap. We construct a series of solvable models that ground states are short-range SU(4)-RVB states. The results are generalized to the antiferromagnetic SU(N) models.
To describe the spin-orbital energy gap formation in the one-dimensional symmetrically coupled spin-orbital model, we propose a simple mean-field theory based on an SU(4) constraint fermion representation of spins and orbitals. A spin-orbital gapped phase is formed due to a marginally relevant spin-orbital valence bond pairing interaction. The energy gap of the spin and orbital excitations grows extremely slowly from the SU(4)-symmetric point up to a maximum value and then decreases rapidly. By calculating the spin, orbital, and spin-orbital tensor static susceptibilities at zero temperature, we find a crossover from coherent to incoherent magnetic excitations as the spin-orbital coupling decreases from large to small values.
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.