  We study the ground state of the one-dimensional "$t$-$J_s$-$J_{\tau}$
model," which is a variant of the $t$-$J$ model with additional channel degree
of freedom. The model is not only a generalization of the $t$-$J$ model but
also an effective model of the two-channel Kondo lattice model in the
strong-coupling region. The low-energy excitations and correlation functions
are systematically calculated by the density matrix renormalization group
method, and the ground-state phase diagram at quarter filling consisting of a
Tomonaga-Luttinger liquid, spin-gap state, channel-gap state, insulator, and
phase separation is determined. We find that weak channel fluctuations
stabilize the spin-gap state, while strong channel fluctuations lead to the
transition to the insulator.
