Orbital liquid in perovskite transition-metal oxides

We study the effects of the degeneracy of the $e_g$ orbitals in perovskite transition-metal oxides in the limit of strong repulsive electron-electron interaction. The isospin field is introduced to describe the orbital degrees of freedom and is represented by the boson with a constraint. The dispersion of this boson is flat along $(\pi /a,\pi {/a,k}_z)$ $(a$: lattice constant) and the other two equivalent directions. This enables the orbital disordered phase down to low temperatures. Some of the anomalous experiments in the low-temperature ferromagnetic phase of La${}_{1-x}$Sr${}_x$MnO${}_3$ are interpreted in terms of this orbital liquid picture. The coupling between the orbital degrees of freedom and the Jahn-Teller lattice distortion and its implications to the optical conductivity are also discussed.