A possible phase diagram of a t-J ladder model

We investigate a t-J ladder model by numerical diagonalization method. By calculating correlation functions and assuming the Luttinger liquid relation, we obtained a possible phase diagram of the ground state as a function of J/t and electron density $n$. We also found that behavior of correlation functions seems to consist with the prediction of Luttinger liquid relation. The result suggests that the superconducting phase appear in the region of $J/t \displaystyle{ \mathop{>}_{\sim}} 0.5$ for high electron density and $J/t \displaystyle{ \mathop{>}_{\sim}} 2.0$ for low electron density.