Valence Bond Crystal and Possible Analog of a Supersolid in a t2g Orbital Model

4 pages + supplementary material (3 pages), 7 figures; International audience; We study an orbital model of localized t2g electrons on the triangular lattice and provide evidence of two distinct strongly fluctuating regimes, depending on type of the interactions. The superexchange regime clearly indicates the presence of a dimerized valence bond crystal phase, obtained through an effective quantum dimer model derived from the orbital Hamiltonian and analyzed numerically. In the opposite direct exchange regime, another effective model adapted to the local constraints is derived --- here the effect of subleading perturbations selects a highly resonating ground state, combining diagonal and off-diagonal long-range orbital orders.