Density Matrix Renormalization Group calculations for the Ising Model with a Transverse Field

Abstract

In this thesis, the Density Matrix Renormalization Group algorithm is introduced. Some key concepts from quantum mechanics are discussed to aid in understanding the method and it is put into the context of the Renormalization Group. The algorithm is discussed from a mostly practical perspective. As a model to test the algorithm, the Ising Model with a Transverse Field was used. This model is interesting because it is one of the simplest one-dimensional models that displays a phase transition at a finite external field. It can also be solved analytically, which makes it possible to easily check the results of DMRG calculations. The DMRG algorithm was implemented from scratch in C++ for the Transverse Field Ising Model. Using this implementation, the errors in DMRG calculations were explored, as well as the phase transition in the Transverse Field Ising Chain.