  We study dilution effects in a Mott insulating state with quantum orbital
degree of freedom, termed the two-dimensional orbital compass model. This is a
quantum and two-dimensional version of the orbital model where the interactions
along different bond directions cause frustration between different orbital
configurations. A long-range correlation of a kind of orbital at each row or
column, termed the directional order, is studied by means of the quantum
Monte-Carlo method. It is shown that decrease of the ordering temperature due
to dilution is much stronger than that in spin models. Quantum effect enhances
the effective dimensionality in the system and makes the directional order
robust against dilution. We discuss an essential mechanism of the dilute
orbital systems.
