GRK 1995: Quantum Many-Body Methods in Condensed Matter Systems

量子力学性质的多体效应不仅在扩展的凝聚态系统中导致重要的涌现集体现象，如超导和磁性，而且在各种介观和纳米系统中也起着至关重要的作用。因此，量子多体物理学构成了一个迷人的基础研究领域，并对应用产生了影响。理论物理学面临着三个挑战：（a）更深入地理解关联效应，并获得（B）更现实的描述以及（c）更精确的涌现现象。我们在RTG的第一个资助期内解决了这些核心问题，我们打算在拟议的第二个资助期内进一步探讨这些问题，最终目标是对功能材料和纳米电子学的发展产生影响。由于通过单一的、高度专业化的现代量子多体方法所能取得的进展是有限的，我们的研究战略是系统地联合收割机互补技术，并利用它们的协同作用。一个例子是从头算和强相关方法在现代材料研究中的联合应用。另一个是最近在量子信息科学中发展起来的方法在多体模型中的应用。在过去，方法组合已经证明了它对某些特定问题的作用。在RTG的第一个供资期间，它在更广泛的技术基础上进行。在这种情况下，博士研究人员的RTG资格计划是实现我们目标的不可或缺的手段。现代量子多体方法，无论是解析的还是数值的，在技术上都具有挑战性。早期的职业研究人员通常在他们的硕士和博士研究中只学习和应用一种方法。利用我们的资格和监督计划，我们的RTG毕业生已经获得了开发和应用的第一手经验，至少有两种这样的技术。亚琛-于利希地区拥有众多的研究人员，在量子多体方法领域拥有悠久而成功的历史，构成了一个理想的环境，支持RTG实现这一具有挑战性的目标。我们有广泛的研究经验，国际合作和地位，以及教学能力，提供广泛和苛刻的RTG计划，因为我们已经在第一个资助期证明。贡献研究人员的专业知识包括面向应用的ab-inito方法，数值多体方法，非平衡技术，重整化群方法以及基于量子信息的方法。

Many-body effects of quantum-mechanical nature not only lead to important emergent collective phenomena in extended condensed matter systems, such as superconductivity and magnetism, but also play a crucial role in various meso- and nanoscopic systems. Quantum many-body physics, thus, constitutes a fascinating field of basic research with implications for applications. Theoretical physics faces three challenges: (a) to gain a deeper understanding of correlation effects and to obtain (b) a more realistic as well as (c) a more precise description of the emergent phenomena. We addressed these central issues in the first funding period of our RTG, and we intend to pursue them further in the proposed second period, with the ultimate goal of having an impact on the development of functional materials and nano-electronics. Since the progress, which can be achieved through a single, highly specialized modern quantum many-body method, is limited, our research strategy is to systematically combine complementary techniques and to exploit their synergy. An example is the combined application of ab-initio and strongly correlated methods to investigate modern materials. A further one is the application of methods developed recently in quantum information science to many-body models. In the past, method combination has proved its power for certain, selected problems. During the first funding period of the RTG, it was pursued on a much broader basis of techniques. In this context, the RTG qualification program for doctoral researchers is an indispensable means of attaining our goals. Modern quantum many-body methods, both analytical as well as numerical, are technically challenging. Early career researchers usually learn and apply only one method in their Master’s and PhD studies. Taking advantage of our qualification and supervision program, our RTG graduates have gained first-hand experience in the development and application of, at least, two such techniques. The Aachen-Jülich area, with its many researchers and its long and successful history in the field of quantum many-body methods, constitutes an ideal environment sustaining a RTG with this challenging aim. We have broad research experience, international collaborations and standing, as well as the teaching capacity to offer an extensive and demanding RTG program, as we have demonstrated in the first funding period. The expertise of the contributing researchers covers application-oriented ab-inito methods, numerical many-body approaches, non-equilibrium techniques, renormalization group methods, as well as quantum information based approaches.