Quantum Fluctuation Induced Order in an Anisotropic Pseudospin Model

A model describing orbital degrees of freedom of e g electrons on a cubic lattice is studied at half-filling. The orbital degrees of freedom can be described by pseudospins, and the ground state and the excitation spectrum of the effective Hamiltonian in the strong coupling limit are studied. It is found that a pseudospin ordered state is realized at finite temperatures with the help of the quantum fluctuations, which yield a finite gap in the purely two-dimensional excitation spectrum.