Master's Defense: Raffael Gawatz

Title: Matrix Product State Based Algorithms for Ground States and Dynamics


Strongly correlated systems are arguably one of the most studied systems in condensed matter physics. Yet, the (strong) interaction of many particles with each other is most of the times a strong limitation on practicable analytical methods, such that usually collective phenomenas are studied. To overcome this limitation, numerical techniques become more and more inde- spensable in the study of many-body systems. A fast growing field of numerical techniques which relies on the notion of entanglement in strongly correlated systems thoroughly analyzed in this thesis is usually referred to as Matrix Product States routines (in one dimension).

In the following we will present such different numerical Matrix Product State routines and apply them to several interesting pehnomena in the field of condensed matter physics. Hereby, the motivation is to verify the accuracy of the implemented routines by matching them with well established results of interesting physical models. The algorithms will cover the exact computation of ground states as well as the dynamics of strongly correlated systems. Further, effort has been put in pointing out for which systems the routines work best and where pos- sible limitations might occure. In this manner the with our routines studied physical models, will complete the picture by giving some hands-on examples for systems worth studying with Matrix Product State algorithms.