  The ground state of the one-dimensional dimerized $t$$-$$J$ model at quarter
filling is studied by a Lanczos exact-diagonalization technique on small
clusters. We calculate the charge gap, spin gap, binding energy,
Tomonaga-Luttinger-liquid parameter, Drude weight, anomalous flux quantization,
etc. We thereby show that the two types of dimerization, i.e., a dimerization
of hopping integral and a dimerization of exchange interaction play a mutually
competing role in controlling the ground state of the system and this leads to
the emergence of various phases including the Mott insulating,
Tomonaga-Luttinger-liquid, and Luther-Emery-liquid phases. The ground-state
phase diagram of the model is given on the parameter space of the
dimerizations.
