Density matrix renormalization group

Abstract

The dimension of the Hilbert space of many-body quan- tum system increases exponentially with the number of particles. When there is the possibility of having the variable number of particles at each position, then the di- mension of Hilbert space increases exponentially with the number of possible position a particle can acquire,called as the site. Due to this reason, the exact diagonaliza- tion simulation of systems in condensed matter physics is impossible for a large size system. For most of the sys- tem in condensed matter physics, the analytical solution does not exist. Hence, one must find a way to simulate these many-body interacting system. Here we discuss a numerical algorithm which is designed to solve the many- body quantum system with excellent accuracy. In this article, we will discuss the algorithm as well as results obtained by the algorithm for one-dimensional Tight- binding model and one dimensional Heisenberg chain