DMRG Studies of Frustrated and Doped Systems

材料研究部和化学部共同资助该奖项，该奖项支持理论和计算研究和教育，旨在了解凝聚态物质和化学系统，这些系统拥有强烈相互作用的电子，其行为受量子力学控制。对这些系统的量子行为的基本理解对于开发具有定制性质的新材料和分子至关重要，也可以导致预测新的物质状态。开发用于求解描述许多相互作用组分的系统的量子力学方程的新算法和软件仍然是最重要的理论技术之一。PI是这些算法中最突出的算法之一，密度矩阵重整化群（DMRG）的发明者，并继续开发ITensor，这是一个广泛使用的软件库，用于执行这些计算。在PI工作的基础上，一个大型的国际科学家小组将DMRG扩展到一个新的物理学领域，张量网络，其应用范围从化学到黑洞物理学和量子引力理论。PI目前的工作重点是量子自旋液体和高温超导性。自旋液体是一种新的物质状态，其不寻常的性质可以使量子计算机的建立成为可能，它可以比任何现有的计算机以指数速度解决某些问题。高温超导性对于基本原因和应用都很重要。从概念上讲，理解高温超导性是如何工作的被认为是凝聚态物理学中最重要的问题之一。高温超导体已经被用于许多重要的应用，如无线通信和电力传输。揭示高温超导性如何在某些材料中出现，可能有助于创造长期寻求的室温超导体。这项研究为培养下一代理论科学家提供了极好的机会。ITensor软件库的进一步发展使DMRG和张量网络方法变得可用，并对广泛的科学家有用，而不必自己开发软件。技术总结材料研究部和化学部共同资助该奖项，支持旨在理解凝聚态、冷原子和化学系统中强相互作用量子系统的研究和教育。这项工作主要包括模拟模型系统和开发新的算法，使这些模拟。这项工作的主要应用是受抑自旋系统和掺杂费米子系统（如高温超导体），这些系统受到使量子蒙特卡罗方法无效的符号问题的困扰。特别令人感兴趣的是自旋液体系统，这是一种可以发生在受抑自旋系统中的新物质状态。自旋液体具有拓扑有序性，它们的不寻常性质可以用来消除消相干，这是创建量子计算机的一个要求。实验研究有时无法区分无序自旋系统和真正的量子自旋液体;这个项目将澄清哪些系统是真正的量子自旋液体。该项目还涉及研究高温超导体，特别是条纹和其他具有超导性的不均匀性之间的竞争，以及赝能隙相的性质。特别令人感兴趣的是研究电子之间的长程库仑相互作用及其对条纹和超导性之间竞争的影响。PI是密度矩阵重整化群（DMRG）的发明者，这是模拟一维系统的领先算法之一。在过去的十年中，DMRG已经成为一个更大的领域，张量网络的一部分，并与量子信息科学密切相关。PI在算法方面的工作现在包含了张量网络的许多想法。PI将进一步开发ITensor，这是一个广泛使用的软件库，用于进行DMRG和张量网络计算。这项研究为培养下一代理论科学家提供了极好的机会。ITensor软件库的进一步发展使DMRG和张量网络方法变得可用，并对广泛的科学家有用，而不必自己开发软件。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARY The Division of Materials Research and the Chemistry Division jointly fund this award, which supports theoretical and computational research and education aimed at understanding condensed-matter and chemical systems that host strongly interacting electrons whose behavior is governed by quantum mechanics. Fundamental understanding of the quantum behaviors of these systems is crucial for developing novel materials and molecules with tailored properties and can also lead to the prediction of new states of matter.The development of novel algorithms and software for solving the equations of quantum mechanics that describe systems of many interacting constituents remains one of the most important theoretical techniques. The PI is the inventor of one of the most prominent of these algorithms, the density matrix renormalization group (DMRG), and continues developing ITensor, a widely used software library for carrying out these calculations. Building on the PI's work, a large international group of scientists has extended DMRG to a new field of physics, tensor networks, with applications ranging from chemistry to the physics of black holes and to the quantum theory of gravity. The PI's current work is focused on quantum spin liquids and on high-temperature superconductivity. Spin liquids are a novel state of matter whose unusual properties could enable building a quantum computer, which can solve certain problems exponentially faster than any currently existing computer. High-temperature superconductivity is important for both fundamental reasons as well as for applications. Conceptually, understanding how high-temperature superconductivity works is considered one of the most important problems in condensed matter physics. High-temperature superconductors are already used in a number of important applications, such as wireless communications and power transmission. Unraveling how high-temperature superconductivity emerges in certain materials might enable the creation of long-sought room-temperature superconductors.This research provides excellent opportunities for training the next generation of theoretical scientists. The further development of the ITensor software library is making DMRG and tensor-network methods available and useful for a broad range of scientists that will not have to develop the software themselves.TECHNICAL SUMMARYThe Division of Materials Research and the Chemistry Division jointly fund this award, which supports research and education aimed at understanding strongly interacting quantum systems in condensed matter, cold atoms, and chemical systems. The work consists primarily of simulating model systems and of developing new algorithms for enabling these simulations. The primary application of the work is to frustrated spin systems and to doped fermion systems (such as the high-temperature superconductors), which suffer from the sign problem that makes quantum Monte Carlo methods ineffective. Of particular interest are spin liquid systems, a novel state of matter that can occur in frustrated spin systems. Spin liquids exhibit topological order, and their unusual properties could be used for eliminating decoherence, a requirement for creating a quantum computer. Experimental studies sometimes cannot distinguish between disordered spin systems and true quantum spin liquids; this project will clarify which systems are true quantum spin liquids. The project also involves studying high-temperature superconductors, in particular the competition between stripes and other inhomogeneities with superconductivity, and the nature of the pseudogap phase. Of particular interest is studying the effect of long-range Coulomb interactions between electrons and their effect on the competition between stripes and superconductivity.The PI is the inventor of the density matrix renormalization group (DMRG), one of the leading algorithms for simulating 1D systems. Within the last decade, DMRG has become part of a larger field, tensor networks, and has become closely associated with quantum information science. The PI's work in algorithms now incorporates many of the ideas of tensor networks. The PI will further develop ITensor, a widely used software library for carrying out DMRG and tensor network calculations.This research provides excellent opportunities for training the next generation of theoretical scientists. The further development of the ITensor software library is making DMRG and tensor-network methods available and useful for a broad range of scientists that will not have to develop the software themselves.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.