Spontaneous spin stripe dimerization in the doped t-J model

To investigate spin dimerization in the t-J model we consider the extended t-J-\delta model with explicit spin dimerization introduced via parameter \delta. At zero doping the dimerized spin liquid is unstable at \delta < \delta_c = 0.3. We demonstrate that the doping stabilizes the dimerized stripe phase: the \delta_c(x) decreases when doping x increases. At doping larger than critical, x > x_c, the dimerized phase is stable even without explicit dimerization, i.e. at \delta=0.