Quantum Melting of Magnetic Order due to Orbital Fluctuations

We have studied the phase diagram and excitations of the spin-orbital model derived for a three-dimensional perovskite lattice, as in ${\mathrm{KCuF}}_3$. The results demonstrate that the orbital degeneracy drastically increases quantum fluctuations and suppresses the classical long-range order near the multicritical point in the mean-field phase diagram. This indicates the presence of a quantum liquid state, and we present explicit evidence for valence bond type correlations in three dimensions.