Computational Quantum Condensed Matter

该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。 许多材料显示出挫折和强相关效应，从而产生新的相和性质，这是目前深入研究的焦点。本质上，我们这样说的意思是，系统作为一个整体具有单个部分所不具有的属性。当我们对这种材料进行建模时，很明显，分析计算是困难的，而且往往不可靠，唯一可行的替代方案是使用计算机进行大规模模拟。 在这里，它建议将这种方法应用到这样的强相关性和挫折是重要的问题，如量子自旋链，挫折磁铁，超导电性和其他强相关或无序系统。特别是，它建议调查自旋液体和其他外来相，因为它们发生在这些系统中，以及这些新的阶段的过渡。一个特别重要的方面是纠缠，这是这些材料在低温下固有的量子力学性质的量度。 第二个目标是为这些材料的研究开发新的先进的数值算法。 对纠缠的详细了解已被证明对实现这一目标至关重要。 数值结果的可用性将是相当重要的新材料的发展至关重要的科学竞争力和新的数值技术的发展可能会提高我们的理解或直接解决巨大的挑战计算问题，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.