Dynamics of correlated quantum systems out of equilibrium

失去平衡的相关量子系统的动力学

• 批准号: 453644843
• 负责人: Dr. André Erpenbeck
• 金额: --
• 依托单位: Physics Department
• 依托单位国家: 德国
• 项目类别: WBP Fellowship
• 财政年份: 2021
• 资助国家: 德国
• 起止时间: 2020-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/453644843?language=en
• 关键词: Dynamics; correlated; quantum; systems; out

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.

相关量子多体系统是现代凝聚态物理研究的基础。在实验上，对新材料和量子点系统的研究，特别是在时间依赖影响和非平衡输运条件下的研究，揭示了许多有趣和复杂的现象。迄今为止，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，在本项目中，我们的目标是发展一种适用于非平衡相关量子系统的预测理论。然后使用这种方法来提供对相关量子系统的特定行为的全面理解。从方法论的角度来看，我们的目标是将特定的量子蒙特卡罗方法与扩展的动态平均场理论相结合。量子蒙特卡罗方法可以描述量子杂质模型的动力学，这是一个与环境相互作用的量子系统，以统计方式考虑所有可能的行为。依靠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，我们提供了对非平衡量子系统中相关性影响的深入微观理解。因此，我们受益于非平衡输运动力学领域的专业知识。随后，我们利用动态平均场理论将杂质模型积累的洞察力转移到扩展固体和晶格模型领域。这种量子嵌入方法也适用于本项目的范围，它在考虑一个或几个晶格点作为杂质并确定晶格动力学作为该杂质的自洽解时，提供了晶格模型的描述。因此，这种方法直接提供了对扩展系统中相关性角色的微观理解。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制度。