DMRG Studies of Frustrated and Doped Systems

该奖项支持理论和计算研究，以及旨在理解凝聚态物质和涉及许多可以用量子力学描述的强相互作用电子的化学系统的教育。 了解这些系统是开发新材料和分子的关键，这些材料和分子可以预测新的物质状态，并设计具有有用特性的新材料。取得理论进展的最重要的技术之一是开发新的计算机算法和软件，用于求解描述许多相互作用粒子系统的量子力学方程。PI发明了一种重要的算法，密度矩阵重整化群（DMRG），并且是执行计算的软件库ITensor的开发者。在这项工作的基础上，一个国际科学家小组将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和量子引力。 该奖项支持专注于新物质状态，量子自旋液体和高温超导性的研究。当由于海森堡的不确定性原理导致的量子力学波动将材料中的任何磁性痕迹融化到绝对零度时，就会产生量子自旋液体，留下具有不寻常性质的液体，可以为构建量子计算机提供基础。量子计算机被预测能够比任何现有的计算机以指数速度解决某些问题。高温超导体可以在比其他已知超导体更高的温度下无损耗地传输电流，但仍然几乎在氮气为液体的温度下。 当前的应用包括无线通信和电力传输。了解电子如何自组织进入高温超导状态是一个重要的问题，可能导致在室温下的超导体。这项研究为培养下一代理论和计算科学家提供了机会。ITensor软件库为来自不同研究领域的科学家提供DMRG技术和张量网络的访问权限，并构成材料研究和化学社区网络基础设施的一部分。技术概述该奖项支持理论和计算研究，以及旨在理解强相互作用量子凝聚态，冷原子和化学系统的教育。该研究涉及模拟模型系统和开发用于这些模拟的新算法，主要集中在受抑自旋系统和掺杂费米子系统，如高温超导体。为了避免量子蒙特卡罗方法的符号问题，PI计划利用密度矩阵重整化群方法。 特别令人感兴趣的是自旋液体系统，这是一种可以在表现出挫折的自旋系统中发生的新的物质状态。 自旋液体具有拓扑有序性，它们的特殊性质可以用来消除量子计算机中的退相干势垒。该项目还涉及高温超导体的研究，重点是非均匀相之间的竞争，包括具有超导性的条纹，以及赝能隙相的性质。PI发明了密度矩阵重整化群（DMRG），这是模拟一维系统的领先算法。 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。 大多数应用工作使用DMRG，而不是一些较新的张量网络方法，因为DMRG仍然非常有效。 PI是用于执行DMRG和张量网络计算的领先软件库ITensor的开发商。这项研究为培训下一代理论和计算科学家提供了机会。ITensor软件库为来自不同研究领域的科学家提供了访问DMRG技术和张量网络的机会，并成为材料研究和化学社区网络基础设施的一部分。

NON-TECHNICAL SUMMARY This award supports theoretical and computational research, and education aimed at understanding condensed matter and chemical systems involving many strongly interacting electrons which can be described by quantum mechanics. Understanding these systems is key to developing novel materials and molecules that can lead to the prediction of new states of matter, and to designing new materials with useful properties. One of the most important techniques for making theoretical progress is the development of novel computer algorithms and software for solving the equations of quantum mechanics that describe systems of many interacting particles. The PI has invented an important algorithm, the density matrix renormalization group (DMRG), and is the developer of a software library for carrying out the calculations, ITensor. Building on this work, an international group of scientists has extended DMRG to a new field of physics, Tensor Networks, with applications ranging from chemistry to black holes and quantum gravity. This award supports research focused on novel states of matter, quantum spin liquids and high temperature superconductivity. Quantum spin liquids result when quantum mechanical fluctuations due to Heisenberg's uncertainty principle melt away any trace of magnetism in a material down to the absolute zero of temperature, leaving a liquid with unusual properties that could provide the foundation for building a quantum computer. A quantum computer is predicted to be able to solve certain problems exponentially faster than any currently existing computer. High temperature superconductors can transport electric current without loss at higher temperatures than other known superconductors, but still almost at temperatures where nitrogen is a liquid. Current applications include wireless communications and power transmission. Understanding how electrons self-organize into the high temperature superconducting state is an important problem that may lead to superconductors at room temperature. This research provides opportunities for training the next generation of theoretical and computational scientists. The ITensor software library provides a scientists from different research areas access to DMRG techniques and tensor networks and forms part of the cyberinfrastructure of the materials research and chemistry communities.TECHNICAL SUMMARYThis award supports theoretical and computational research, and education aimed at understanding strongly interacting quantum condensed matter, cold atom, and chemical systems. The research involves simulating model systems and developing new algorithms for these simulations, and is focused primarily on frustrated spin systems and doped fermion systems like high temperature superconductors. To avoid the sign problem of quantum Monte Carlo methods, the PI plans to utilize density matrix renormalization group methods. Of particular interest are spin liquid systems, a novel state of matter that can occur in spin systems that exhibit frustration. Spin liquids have topological order, and their unusual properties could be used for eliminating the barrier of decoherence in building a quantum computer. This project also involves studying the high temperature superconductors, with a focus on the competition among inhomogeneous phases including stripes with superconductivity, and on the nature of the pseudogap phase.The PI invented the density matrix renormalization group (DMRG), a leading algorithm 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. The PI's work in algorithms now incorporates many of the ideas of tensor networks. Most of the application work uses DMRG rather than some of the newer tensor network methods, as DMRG continues to be very effective. The PI is the developer of a leading software library for carrying out DMRG and tensor network calculations, ITensor.This research provides opportunities for training the next generation of theoretical and computational scientists. The ITensor software library provides a scientists from different research areas access to DMRG techniques and tensor networks and forms part of the cyberinfrastructure of the materials research and chemistry communities.