Resonating valence-bond state in an orbitally degenerate quantum magnet with dynamical Jahn-Teller effect

Short-range resonating valence-bond states in an orbitally degenerate magnet on a honeycomb lattice are studied. A quantum-dimer model is derived from the Hamiltonian which represents the superexchange interaction and the dynamical Jahn-Teller (JT) effect. We introduce two local units termed "spin-orbital singlet dimer," where two spins in a nearest-neighbor bond form a singlet state associated with an orbital polarization along the bond, and "local JT singlet," where an orbital polarization is quenched due to the dynamical JT effect. A derived quantum-dimer model consists of the hopping of the spin-orbital singlet dimers and the JT singlets, and the chemical potential of the JT singlets. We analyze the model by the mean-field approximation, and find that a characteristic phase, termed "JT liquid phase," where both the spin-orbital singlet dimers and the JT singlets move quantum mechanically, is realized. Possible scenarios for the recently observed non-magnetic-ordered state in Ba3CuSb2O9 are discussed.