DMRG studies of frustrated and doped systems

该奖项支持使用密度矩阵重整化群进行二维受挫磁系统和强相关掺杂电子系统的理论和计算工作。材料研究中一个令人兴奋的领域是对低维系统中强相关效应的研究。这些体系表现出广泛的行为，如高温超导、反铁磁性、条纹和自旋液相。数值模拟技术对于理解这些系统变得越来越必要，因为这些系统具有强耦合项和不同类型顺序之间的竞争。密度矩阵重整化群是研究强相关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这样的系统，包括自旋链、阶梯和二维簇，无论是自旋系统还是掺杂系统。在此期间，重点将越来越多地集中在足够大的集群上，从而可以将结果外推到无限大小的极限。将在理解量子自旋液体方面作出实质性的努力，继续前一时期的工作，其中kagome Heisenberg模型被证明具有自旋液体基态。kagome模型将进一步研究，特别是在具有次近邻相互作用的广义形式下。除了在更大的参数空间中绘制相图外，还将研究初等激励和拓扑顺序的性质。此外，其他受挫自旋系统，如蜂窝晶格上具有受挫次近邻相互作用和交换各向异性的海森堡模型，将被研究。PI将扩展并进一步开发一个公共可用的软件库，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，智能张量。这个图书馆的最初工作是在以前的NSF的支持下开始的，并且已经取得了实质性的进展。该合同下的工作将侧重于使库易于非专业人员使用，同时通过新的并行算法增加其功能。该奖项支持旨在理解物质奇异量子态的理论和计算研究与教育。有人可能会认为，在绝对零度之前，一切都是冻结的。然而，液氦即使在绝对零度的大气压力下仍保持液态，但它是唯一能保持液态的物质。液氦之所以不会凝固，是因为原子不断的量子力学波动克服了它们非常微弱的吸引力。冻结成固体是一种秩序。那磁性呢？在绝对零度下，磁性材料中所有的微观磁铁都必须排成一列才能成为磁铁吗？在绝对零度不能成为磁铁的假想磁系统称为“自旋液体”。从实验和理论上寻找自旋液体已经有一段时间了。最近的一项令人兴奋的研究表明，一种名为赫伯特史密斯石的不寻常矿物似乎是一种自旋液体。PI最近为最适合赫伯特史密斯理论模型的自旋液体提供了证据。PI的目标是继续探索这个模型，同时寻找其他可能是自旋液体的材料模型。除了研究自旋液体外，PI还将利用他的数值技术研究高温超导性和一维磁系统。自旋液体可能是理解受挫的磁性材料和发现可能导致新技术的物质的新电子状态的关键。自旋液体也可能阐明超导的机制，超导是一种电子物质的状态，可以在不损失的情况下携带电流，使超导在更高的温度下具有潜在的应用于电力传输。

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.