Dynamics of correlated quantum systems out of equilibrium

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Correlated quantum many-body systems are of fundamental interest in modern condensed matter physics. Experimentally, studies on new materials and quantum dot systems, especially under time-dependent influences and nonequilibrium transport conditions, have revealed a multitude of interesting and intricate phenomena. To date, a large extent of these effects is not well understood and the relevant degrees of freedom and their effective description are controversially debated.Consequently, a theoretical and conceptual framework is required which is capable of describing these systems and explaining their dynamics. Therefore, within this project, we aim at developing a predictive theory which is applicable to correlated quantum systems out of equilibrium. This methodology is then employed to provide a comprehensive understanding of the particular behavior of correlated quantum systems.From a methodological point of view, we aim at combining a particular quantum Monte Carlo approach with an extended dynamical mean field theory. Quantum Monte Carlo methods can describe the dynamics of a quantum impurity model, that is a quantum system which interacts with an environment, upon considering all possible behaviors in a statistical manner. Relying on a well established quantum Monte Carlo approach and extending its applicability to the corresponding systems and timescales, we provide a deepened microscopic understanding of the influence of correlations in quantum systems out of equilibrium. Thereby, we profit from the expertise of the field of nonequilibrium transport dynamics. Subsequently, we transfer the insight accumulated for impurity models to the realm of extended solids and lattice models using the dynamical mean field theory. This quantum embedding approach, which is also generalized for the scope of this project, provides a description for lattice models upon considering one or several lattice sites as an impurity and determining the lattice dynamics as the self-consistent solution of this impurity. As such, this approach directly provides a microscopic understanding of the role of correlations in extended systems. Overall, we foresee that the new method has the capacity to answer a variety of fundamental questions related to correlated quantum systems, as it has the ability to explore systems and parameter regimes which can not be addressed by any other state-of-the-art technique.