Dynamics of correlated quantum systems out of equilibrium

关联量子多体系统是现代凝聚态物理学中的一个基本问题。在实验上，对新材料和量子点系统的研究，特别是在时间相关影响和非平衡输运条件下的研究，揭示了许多有趣而复杂的现象。到目前为止，这些影响在很大程度上还没有得到很好的理解，相关的自由度及其有效描述也存在争议，因此，需要一个能够描述这些系统并解释其动态的理论和概念框架。因此，在这个项目中，我们的目标是发展一个预测理论，适用于相关的量子系统的平衡。从方法论的角度来看，我们的目标是将一种特殊的量子Monte Carlo方法与一种扩展的动力学平均场理论相结合。量子蒙特卡罗方法可以描述量子杂质模型的动力学，即在以统计方式考虑所有可能的行为时，与环境相互作用的量子系统。依赖于一个完善的量子蒙特卡罗方法，并将其适用性扩展到相应的系统和时间尺度，我们提供了一个深入的微观理解的量子系统中的相关性的影响失去平衡。因此，我们受益于非平衡输运动力学领域的专业知识。随后，我们转移的洞察力积累的杂质模型领域的扩展固体和晶格模型，使用动力学平均场理论。这种量子嵌入的方法，这也是广义的本项目的范围内，提供了一个描述的晶格模型，考虑一个或几个晶格网站作为一种杂质，并确定晶格动力学作为自洽的解决方案，这种杂质。因此，这种方法直接提供了对扩展系统中相关性作用的微观理解。总的来说，我们预见新方法有能力回答与相关量子系统相关的各种基本问题，因为它有能力探索任何其他最先进技术无法解决的系统和参数机制。

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.