Tetramerization in a SU(4)-Heisenberg model on the honeycomb lattice

The SU(4) Heisenberg model can serve as a low energy model of the Mott insulating state in materials where the spins and orbitals are highly symmetric, or in systems of alkaline-earth atoms on optical lattice. Recently, it has been argued that on the honeycomb lattice the model exhibits a unique spin-orbital liquid phase with an algebraic decay of correlations [P. Corboz et al., Phys. Rev. X 2, 041013 (2012)]. Here we study the instability of the algebraic spin-orbital liquid toward spontaneous formation of SU(4) singlet plaquettes (tetramerization). Using a variational Monte Carlo approach to evaluate the projected wave-function of fermions with $\pi$-flux state, we find that the algebraic liquid is robust, and that a finite value of the next nearest exchange is needed to induce tetramerization. We also studied the phase diagram of a model which interpolates between the nearest neighbor Heisenberg model and a Hamiltonian for which the singlet-plaquette product state is an exact ground state.