  By using the density matrix renormalization group method, we investigate
ground- and excited-state properties of the e_g-orbital degenerate Hubbard
model at quarter filling for two kinds of lattices, zigzag chain and ladder. In
the zigzag chain, the system is effectively regarded as a decoupled double
chain of the S=1/2 antiferromagnetic Heisenberg model, and the spin gap is
approximately zero, similar to the case of weakly coupled Heisenberg chains. On
the other hand, in the ladder, the spin correlation on the rung remains robust
and the spin gap exists.
