Computational Quantum Condensed Matter

本提案的目的是应用最先进的数值技术来模拟新材料，特别是所谓的强相关效应或挫折是重要的材料。许多材料表现出挫折和强相关效应，从而产生新的相和性质，这是目前研究的热点。本质上，我们这样说的意思是系统作为一个整体拥有单个部分所不具备的属性。当我们对这些材料进行建模时，很明显，分析计算是困难的，而且往往是不可靠的，唯一可行的替代方法是使用计算机进行大规模模拟。在这里，我们建议将这种方法应用于强相关性和受挫感很重要的问题，如量子自旋链、受挫磁铁、超导和其他强相关或无序系统。特别提出了研究自旋液体和其他外来相，因为它们出现在这些系统以及过渡到这些新相。一个特别重要的方面是纠缠，这是对这些材料在低温下固有量子力学性质的测量。第二个目标是开发新的先进的数值算法来研究这些材料。事实证明，对纠缠的详细理解对实现这一目标至关重要。数值结果的可用性对于开发对我们的科学竞争力至关重要的新材料具有相当的重要性，新的数值技术的发展可能会提高我们的理解或直接解决重大的计算问题，如符号问题，并可能导致新的并行编程范式。

The objective of this proposal is to apply state of the art numerical techniques to simulate new materials, in particular materials where so called strong correlation effects or frustration are important. Many materials display frustration and strong correlation effects giving rise to novel phases and properties that is currently the focus of intense study. In essence, what we mean by this is that the system as a whole possess properties that the individual parts do not have. When we model such materials it becomes apparent that analytical calculations are difficult and often unreliable and the only viable alternative is to perform large scale simulations using computers. Here it is proposed to apply this approach to problems where such strong correlations and frustration are important, such as quantum spin chains, frustrated magnets, supercondcutivity and other strongly correlated or disordered systems. In particular it is proposed to investigate spin liquid and other exotic phases as they occur in these systems as well as the transition into these novel phases. An aspect of special importance is the entanglement, a measure of the inherent quantum mechanical nature of these materials at low temperatures. A secondary objective is to develop new advanced numerical algorithms for the study of these materials. A detailed understanding of entanglement has proven crucial for this objective. The availability of numerical results would be of considerable importance for the development of new materials vital to our scientific competitiveness and the development of new numerical techniques might improve our understanding or directly solve grand-challenge computational problems, such as the sign problem, and could lead to new parallel programming paradigms.