Abstract
The study of many-body systems is important for the properties of material and often has the difficulty in the exponential growth of Hilbert space with system size, especially for those strongly correlated systems which exhibit exotic behavior. However, in the past two decades have developed some useful algorithms of tackling many-body problems, which is not restricted by the growth of system size. The Density Matrix Renormalization Group (DMRG) invented by Steven R. White is the significant one and it is the major algorithm we discuss in this thesis. In addition, this thesis will show the entanglement properties of many-body systems in one dimension which attracts a lot of attention in recent years.