The Development Of DMRG Method And Its Application In One Dimensional Extended T-J Model

t-J model is one of the most important theoretical models among strongly correlated electronic systems, this model becomes especially important when acting as plane method to describe the high-temperature superconducting cuprate. Although the importance of this model lies in its two-dimensional form, the studies on one-dimensional cases show that in one-dimensional form the superconducting phase, which we concerned most, exists in ground state. This allows us to research some of two-dimensional problems by studying one-dimensional cases. For two-dimensional t-J model, there is no entirely convincing approach, but for one-dimensional cases, the density matrix renormalization group method can get result approximating to exact solution.With the development of experimental techniques, cold atom physics is very active in both theoretical and experimental field. Recently, A. V. Gorshkov and other researchers proposed a method to use ultracold polar molecules to simulate extending t-J model which was approved by experiments. We use density matrix renormalization group numerical value to compute this model and compare with the experimental results, in order to confirm the feasibility of the program, and hope to have a certain reference value for the later experimental programs.Our computing result shows that the phase diagram to extend t-J model consists of four parts: Lutinger liquid phases with both dominated repulsive and attractive interactions, the metallic phase and the superconducting phase. In the low density region, superconducting pairing of singlet and triplet state will open up a spin energy gap and form a spin gap state. Continuing to strengthen interaction, kinetic energy of the system will be gradually frozen, and strange phenomenon of phase separation will emerge. These results are qualitatively consistent with the traditional t-J model, but in the low density area, superconducting pairing is easier to form, system is faster to get into the superconducting phase as J increases. In the high density region, superconducting pairing was suppressed instead.