Computational Quantum Condensed Matter

这项建议的目的是应用最先进的数值技术来模拟新材料，特别是那些所谓的强关联效应或受挫很重要的材料。许多材料表现出挫折性和强烈的关联效应，导致了新的物相和性能，这是目前研究的重点。本质上，我们这样说的意思是，系统作为一个整体拥有个别部分所不具备的属性。当我们对这种材料建模时，很明显，分析计算是困难的，而且往往是不可靠的，唯一可行的替代方案是使用计算机进行大规模模拟。这里建议将这种方法应用于强关联和受挫很重要的问题，例如量子自旋链、受挫磁体、超导性和其他强关联或无序系统。特别是，有人建议研究在这些系统中出现的自旋、液体和其他奇异相，以及向这些新相的转变。一个特别重要的方面是纠缠，这是一种测量这些材料在低温下固有的量子力学性质的指标。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，对纠缠的详细了解对实现这一目标至关重要。数值结果的可用性将对开发对我们的科学竞争力至关重要的新材料具有相当重要的意义，新的数值技术的开发可能会提高我们的理解或直接解决重大挑战的计算问题，如符号问题，并可能导致新的并行编程范例。

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.