Dynamical effects and non-equilibrium in correlated quantum systems within the framework of matrix product states and renormalization group

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This proposal is targeted towards dynamical effects such as real-time evolution and nonequilibrium effects in strongly correlated quantum-many-body systems. The emphasis lies on periodically driven quantum impurity systems as well as transport through quantum systems coupled to leads at finite voltage bias. In both cases, the system is driven towards a non-equilibrium steady state, the properties of which are strongly debated in current literature given the very limited number of tools for their analysis. My expertise lies within numerical renormalization group theories. The numerical codes in that respect I have developed through the past few years on the broad and general basis of matrix product states strongly discussed also in the context of quantum information science. The projects outlined here therefore can clearly build on this existing expertise. Given the complexity of the topics described, it would be considered a clear milestone in the description of these systems if a reliable non-perturbative treatment of non-equilibrium steady states emerges that can go beyond simple models for very specific parameter settings.