Ground-state phase diagram of the one-dimensional dimerized t-J model at   quarter filling
  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. 
S. Nishimoto and Y. Ohta (Chiba Univ.)