Numerical study of t_2g orbital system with ferromagnetic polarization

Finite-temperature orbital state in a ferromagnetic Mott insulator with triply degenerate t_2g orbital is investigated numerically. We employ the quantum Monte Carlo simulation with the loop algorithm. Indications for conventional staggered-type orbital order are not remarkable down to the lowest temperature to which the present simulation can get access. Physical parameters monitoring the off-diagonal orbital order, which is characterized by a linear combination of the (d_yz, d_zx, d_xy) orbital-wave functions with equal weights, are not conspicuous. It is found that an orbital gaplike behavior appears in the uniform orbital susceptibility. This is supported by a threshold behavior in the staggered correlation function in a calculation with the additional Ising-type interaction. Some rigorous remarks for the long-range orbital order are also presented.