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产生了重要的集体现象，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，量子多体物理构成了一个具有应用意义的迷人的基础研究领域。理论物理面临着三个挑战：(A)对关联效应有更深入的了解，(B)对新出现的现象有更真实的描述，(C)有更准确的描述。我们在RTG的第一个资助期解决了这些核心问题，我们打算在拟议的第二个资助期进一步探讨这些问题，最终目标是对功能材料和纳米电子的发展产生影响。由于通过单一的、高度专业化的现代量子多体方法取得的进展是有限的，我们的研究战略是系统地结合互补技术并利用它们的协同作用。一个例子是从头算方法和强关联方法在现代材料研究中的结合应用。另一个是最近发展起来的量子信息科学方法在多体模型中的应用。在过去，方法组合已经证明了它在特定的、选定的问题上的能力。在RTG的第一个资助期内，它是在更广泛的技术基础上进行的。在这种背景下，博士生研究人员的RTG资格认证计划是实现我们目标不可或缺的手段。现代量子多体方法，无论是解析的还是数值的，在技术上都是具有挑战性的。早期职业研究人员在攻读硕士和博士学位时通常只学习和应用一种方法。利用我们的资格认证和监督计划，我们的RTG毕业生在开发和应用至少两项此类技术方面获得了第一手经验。Aachen-Jülich地区拥有众多的研究人员，在量子多体方法领域有着悠久而成功的历史，构成了支持具有这一挑战性目标的RTG的理想环境。我们拥有广泛的研究经验、国际合作和地位，以及提供广泛和苛刻的RTG计划的教学能力，正如我们在第一个资助期所展示的那样。贡献研究人员的专业知识涵盖了面向应用的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.