| Abstract: | I will give an overview over my results on the description of many-body localized (MBL) systems with quantum circuits – a specific type of tensor networks. I will illustrate how they can be used to quantitatively simulate the controversial two-dimensional MBL phase observed in optical lattice experiments. I will explain why this description captures experimentally relevant time scales, on which two-dimensional MBL is stable. I will also show that quantum circuits can be used to rigorously classify symmetry-protected topological MBL phases in one and two dimensions and to prove their robustness. Finally, I will demonstrate that the conventional notion of local integrals of motion has to be revised for topologically ordered MBL systems. |