Numerical simulation of the dynamics and correlations in quantum many body systems

Abstract

This thesis discusses the application of numerical methods to different complex quantum systems. I present the successful application of the chopped random basis optimal control algorithm (CRAB) to these systems. This includes the optimization of the dynamics of quantum many body systems. For this purpose the possibility of the application of modern tensor network algorithms such as DMRG with the CRAB algorithm is exploited. In all these cases a direct connection to experimental implementations is important to keep. Furthermore, we use these numerical methods to implement a very generic formulation of quantum gauge theories and perform ground state calculations as well as, for the first time, extended dynamical simulations.