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We study a model for orbitally degenerate Mott insulators, where localizedelectrons possess t_2g degrees of freedom coupled by several, competing,exchange mechanisms. We provide evidence for two distinct strongly fluctuatingregimes, depending on whether superexchange or direct exchange mechanismpredominates. In the superexchange-dominated regime, the ground state isdimerized, with nearest neighbor orbital singlets covering the lattice. Byderiving an effective quantum dimer model and analyzing it numerically, wecharacterize this dimerized phase as a valence bond crystal stabilized bysinglet resonances within a large unit cell. In the opposite regime, withpredominant direct exchange, the combined analysis of the original model andanother effective model adapted to the local constraints, shows that subleadingperturbations select a highly resonating ground state, with coexisting diagonaland off-diagonal long-range orbital orders.

Valence Bond Crystal and possible orbital pinball liquid in a t2g model