Abstract
1986 Bednorz and M"uller discovered superconductivity in the rare-earth copper oxides. After one year M.-K.~Wu \textit{et al.} inceased superconducting transition temperature $T_c$ to higher than boiling temperature of liquid nitrogen. These copper oxides (cuprates) are called high temperature superconductors. The layer-structured cuperates are recognized as strongly correlated electronic systems. While Bardeen, Cooper and Schrieffer developed their famous BCS theory, BCS theory fails to explain these unconventional superconductors. The microscopic mechanism of high temperature superconductivity is one of the central problems in condensed matter physics. The dream of theorists is to build a model and to solve everything. However, after devoting themself for decades, many open problems remain. The undoped cuprates are antiferromagnetic insulators and it become superconductors after enough doping electrons or holes. Superconductor-Insulator Transition (SIT) is an important issue in experimental and theoretical research area. Motivated by absence of an SIT driven by correltaion in microscopic models, an interesting model Hamiltonian is investigated in two-leg ladder system by means of Density Matrix Renormalization Group. We focus on the SIT in ground state and attempt to sketch possible phase diagram.