Computing quench dynamics for thermalizing quantum-many body systems in the influence matrix approach

Efficient simulation of quantum many-body systems is the central challenge in the field of computational quantum physics. Recently, an approach based on Feynman and Vernon's influence functional was proposed which allows the computation of local dynamics in interacting systems. In contrast to conventional methods its efficiency relies on the low amount of temporal entanglement instead of spatial entanglement. In this talk we will discuss different types of systems and dynamical regimes where this approach can be sucessfully employed. In particular we analyze thermalizing and many-body localized dynamics in one dimensional systems, as well as transport in interacting heisenberg chains. Finally we will show how to tackle 2D systems using these tools.