摘要
多體系統的研究對於了解材料的性質很重要，但經常有希爾伯特空間(Hilbert space)隨著系統的大小呈指數的成長的困難，特別是那些展現奇特的行為的強關聯系統。然而，在過去的二十年間已經有許多解決多體問題的演算法被發展出來，且這些演算法並不會受限於系統大小的成長。由Steven R. White 所開發的密度矩陣重整化群(Density Matrix Renormalization Group)是最重要的一個，而這個方法也是我們在這個論文裡主要討論的演算法。除此之外，我們在這個論文裡還要討論有關一維多體系統的纏結(entanglement)性質，這在最近數年間吸引了許多的注意。
並列摘要
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.