FOR 1807: Advanced Computational Methods for Strongly Correlated Quantum Systems

量子多粒子系统中的强关联效应对于材料物理、纳米结构和光学晶格中的冷原子等领域中的许多现象都变得越来越重要。数值方法的重大进步使得在理论上处理这些具有物理意义和潜在技术重要性的系统的模型不需要近似值成为可能。这些方法包括量子蒙特卡罗方法、密度矩阵重正化群及其推广方法和自洽动力学团簇方法。该研究股的目的是在德国、奥地利和瑞士形成一个连贯的活跃研究人员网络，他们为数值方法的这一进展作出了重大贡献，以便交流专门知识和想法，并为当前一代高性能计算硬件开发有效的算法。在关联量子系统中长期存在的基本问题，如受挫磁性、掺杂Mott绝缘体以及相互作用的玻色子和耦合的费米子-玻色子系统，有可能取得重大进展。

Strong correlation effects in quantum many-particle systems have become increasingly important for a number of phenomena in domains, which include material physics, nanostructures and cold atoms in optical lattices. Significant advances in numerical methods have made it possible to treat models of these physically interesting and potentially technologically important systems theoretically without approximations. These methods include quantum Monte Carlo, the density-matrix renormalisation group and its generalisations and self-consistent dynamical cluster methods. The aim of this Research Unit is to form a coherent network of active researchers in Germany, Austria and Switzerland, who have made significant contributions to this progress in numerical methods, in order to share expertise and ideas as well as to develop efficient algorithms for the current generation of high-performance computing hardware. There is potential to make significant advances in long-standing fundamental problems in correlated quantum systems such as frustrated magnetism, doped Mott insulators and interacting bosonic and coupled fermion-boson systems.