Numerical study of ground state properties of magnetic disordered systems: Application of Density Matrix Renormalization Group

Abstract

In 1928, K. Wilson was awarded the Nobel prize for his work on the Kondo problem. He was able to solve it through renormalization group method. Unfortunately, the results were not so encouraging, due to their weak accuracy when used to quantum systems. Many attempts were made by physicists: one of them was Steve White, who succeded, after many attempts, to localize the source of failure of Wilson method. In fact, S. White suggested, in a famous paper published in 1993, to use the density matrix concept, which, apparently, helps to choose the ''best'' states that can represent a block as part of a superblock. And it works! Since then, the Density Matrix Renormalization Group (DMRG) has become a powerful tool to investigate the ground state properties of a large panel of quantum systems. The method was also combined to other numerical methods to better understand the behaviour of those systems. Like any other numerical method, DMRG has its own limitations: the most in sight is that it was firstly designed to deal with 1-dimensional systems; even hough, attempts were, later, made to extend it to higher dimensions.