DMRG studies of frustrated and doped systems

该奖项支持使用密度矩阵重整化群的理论和计算工作，用于二维受抑磁系统和强相关掺杂电子系统。 低维系统中强关联效应的研究是材料研究中一个令人兴奋的领域。 这些系统表现出广泛的行为，如高温超导性，反铁磁性，条纹和自旋液相。数值模拟技术已成为越来越有必要了解这些系统，因为系统有很强的耦合条件和不同类型的顺序之间的竞争。密度矩阵重整化群是研究强关联系统最有效的数值方法之一。PI和他的团队将把密度矩阵重整化群应用于各种各样的这些系统，包括自旋链、梯子和二维团簇，无论是自旋系统还是掺杂系统。 这一时期的重点将越来越多地放在足够大的团簇上，结果可以外推到无限大的极限。将在理解量子自旋液体方面做出实质性的努力，继续前一时期的工作，其中kagome海森堡模型被证明具有自旋液体基态。 kagome模型将被进一步研究，特别是在一个广义的形式与次近邻相互作用。除了在较大的参数空间中绘制相图外，还将研究元激发和拓扑序的性质。 此外，其他受抑自旋系统，如蜂窝格子上的海森堡模型与受抑次近邻相互作用，交换各向异性，将被研究。PI将扩展和进一步开发一个公开可用的软件库，适用于许多不同类型的密度矩阵重整化群相关算法。这个库叫做ITensor，意思是智能张量。这个库的最初工作是在以前的NSF支持下开始的，并且已经取得了实质性的进展。 该奖项下的工作将集中在使图书馆易于使用的非专家，同时增加其功能与一个新的并行算法。非技术总结该奖项支持理论和计算研究和教育，旨在了解奇异的量子态的物质。 人们可能会认为，在绝对零度之前，一切都冻结了。 然而，即使在大气压下的绝对零度下，液氦仍然是液体，但它是唯一的物质。液氦不会凝固，因为原子的不断量子力学波动克服了它们非常微弱的吸引力。凝固成固体是一种秩序。磁力呢？磁性材料中的所有微观磁体都必须对齐才能在绝对零度下成为磁体吗？一个假设的磁系统在绝对零度时不能变成磁铁，这种磁系统被称为“自旋液体”。 自旋液体已经在实验和理论上寻找了一段时间。 最近的一项令人兴奋的研究表明，一种名为赫伯特·史密斯的不寻常的矿物似乎是一种自旋液体。PI最近提供的证据自旋液体的理论模型最适合于HerbertSmithite。 PI的目标是继续探索这个模型，并寻找其他可能是自旋液体的材料模型。除了研究自旋液体，PI还将利用他的数值技术研究高温超导和一维磁性系统。自旋液体可能是理解受挫折的磁性材料和发现可能导致新技术的物质新电子态的关键。自旋液体还可以阐明超导性的机制，超导性是一种可以携带电流而不会损失的电子物质状态，使超导性在更高的温度下具有潜在的电力传输应用。

TECHNICAL SUMMARYThis award supports theoretical and computational work using the density matrix renormalization group for two dimensional frustrated magnetic systems and strongly correlated doped electron systems. An exciting area in materials research is the study of strong correlation effects in low dimensional systems. These systems exhibit a wide range of behavior, such as high temperature superconductivity, antiferromagnetism, striped, and spin liquid phases. Numerical simulation techniques have become increasingly necessary to understand these systems, as the systems have strong coupling terms and competition between different types of order. The density matrix renormalization group is one of the most effective numerical techniques for studying strongly correlated systems. The PI and his group will apply density matrix renormalization group to a variety of these systems, including spin chains, ladders, and two-dimensional clusters, both for spin systems and with doping. The focus during this period will be increasingly to large enough clusters that results can be extrapolated to the limit of infinite size.A substantial effort will be made on understanding quantum spin liquids, continuing work of the previous period in which the kagome Heisenberg model was demonstrated to have a spin liquid ground state. The kagome model will be studied further, particularly in a generalized form with next nearest neighbor interactions. In addition to mapping out the phase diagram in the larger parameter space, the nature of the elementary excitations and topological order will be studied. In addition, other frustrated spin systems, such as the Heisenberg model on the honeycomb lattice with frustrated next nearest neighbor interactions, and exchange anisotropies, will be studied.The PI will extend and further develop a publicly available software library appropriate for many different types of density matrix renormalization group related algorithms. The library is called ITensor, for Intelligent Tensor. The initial work for this library was begun with previous NSF support and substantial progress has been made. The work under this award will focus on making the library easy to use for the non-expert, while simultaneously increasing its capabilities with a new parallel algorithm.NONTECHNICAL SUMMARYThis award supports theoretical and computational research and education aimed at understanding exotic quantum states of matter. One might think that everything freezes well before absolute zero in temperature. However, liquid helium remains a liquid even at absolute zero at atmospheric pressure, but it is the only substance which does so. Liquid helium does not solidify because unceasing quantum mechanical fluctuations of the atoms overcome their very weak attraction. Freezing into a solid is one kind of order. What about magnetism? Do the all the microscopic magnets in a magnetic material have to align to become a magnet at absolute zero? A hypothetical magnetic system which fails to become a magnet at absolute zero is called a "spin liquid". Spin liquids have been sought, experimentally and theoretically for some time. A recent excitement shows that an unusual mineral with the name HerbertSmithite seems to be a spin liquid. The PI has recently provided evidence for a spin liquid in the theoretical model most appropriate for HerbertSmithite. The PI aims to continue to explore this model and also look for other models for materials which might be spin liquids. In addition to studying spin liquids, the PI will use his numerical techniques to study high temperature superconductivity and one dimensional magnetic systems.Spin liquids may hold the key toward understanding frustrated magnetic materials and the discovery of new electronic states of matter that may lead to new technologies. Spin liquids may also illuminate the mechanisms for superconductivity, a state of electronic matter that can carry electric current without loss, enabling superconductivity at higher temperatures with potential applications to power transmission.