DMRG Studies of Frustrated and Doped Systems

非技术总结该奖项支持理论和计算研究，以及促进对具有许多相互作用的粒子，特别是电子的量子力学系统的理解的教育。开发新的算法和软件来求解描述由许多相互作用的成分组成的系统的量子力学方程，仍然是最重要的理论技术之一。PI发明了这些算法中最著名的算法之一--密度矩阵重整化群(DMRG)，并继续开发用于执行这些计算的广泛使用的软件库ITInter。在PI工作的基础上，一个庞大的国际科学家小组将DMRG扩展到张量网络，这是一个新领域，应用范围从化学到黑洞物理，再到量子引力理论。PI目前的工作重点是了解高温超导电性，并改进分子和固体量子处理的DMRG方法。在足够低的温度下，一些材料表现出超导电性，这是一种具有有趣和技术有用性质的电子的合作量子状态，能够在其中导电而不损失。大多数已知的超导体在绝对零度附近表现出超导性。高温超导体在氮气变成液体的温度以上表现出超导电性。高温超导电性无论从根本上还是在应用上都是重要的。从概念上讲，理解高温超导的工作原理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。解开某些材料中高温超导电性是如何出现的，可能会创造出人们期待已久的材料，这些材料在室温和普通条件下都表现出超导电性。改进的分子量子处理是量子计算机的主要潜在应用之一，潜在地改进了用于能源应用的药物设计和材料。目前的工作集中在相同的发展，但使用现有的超级计算机而不是量子计算机。这项研究为培养下一代理论科学家提供了极好的机会。进一步的发展使DMRG和张量网络方法可用于科学界，使许多科学领域的发现成为可能。技术总结这个项目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来实现这些模拟。这项工作的主要应用是掺杂费米子系统(如高温超导体)和受挫自旋系统，这些系统存在符号问题，使得量子蒙特卡罗方法无效。PI是密度矩阵重整化群(DMRG)的发明者，DMRG是模拟一维系统的主要算法之一。在过去的二十年里，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融入了张量网络的许多想法。该研究小组还开发了用于进行DMRG和张量网络计算的广泛使用的软件库，并将在该项目中继续开发。这些模拟技术得到了迅速的改进，现在使人们能够更好和更深入地了解高温超导体，特别是条纹和其他不均匀与超导电性之间的竞争，以及伪伽普相的性质。尤其令人感兴趣的是研究电子之间的长程库仑相互作用的影响及其对条纹和超导电性之间的竞争的影响。最近的改进包括更好的动力学和更好的有限温度处理，例如，使用最小纠缠典型热态算法。为了改进分子上的DMRG方法和固体的现实处理，该项目继续致力于开发源于高度局部基集的对角线哈密顿表示。这些对角线表示极大地提高了DMRG的效率。这项研究为培养下一代理论科学家提供了极好的机会。进一步的发展使DMRG和张量网络方法可用于科学界，从而使许多科学领域的发现成为可能。这一奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为是值得支持的。

NONTECHNICAL SUMMARYThis award supports theoretical and computational research, and education to advance understanding of quantum mechanical systems with many interacting particles, particularly electrons. 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 invented 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 tensor networks, a new area with applications ranging from chemistry to the physics of black holes and to the quantum theory of gravity. A focus of the PI's current work is understanding high-temperature superconductivity and improving DMRG methods for quantum treatments of molecules and solids. At sufficiently low temperatures, some materials exhibit superconductivity, a cooperative quantum state of electrons with interesting and technologically useful properties, the ability to conduct electricity without loss among them. Most known superconductors exhibit superconductivity at temperatures near the absolute zero of temperature. High temperature superconductors exhibit superconductivity above the temperature at which Nitrogen becomes a liquid. 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 materials that exhibit superconductivity at room-temperature and under ordinary conditions. Improved quantum treatments of molecules is one of the leading potential applications of quantum computers, potentially improving drug design and materials for energy applications. The current work focuses on the same developments but using current supercomputers rather than quantum computers.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 the scientific community to enable discoveries across many areas of science.TECHNICAL SUMMARYThis project 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 doped fermion systems (such as the high-temperature superconductors) and frustrated spin systems, which suffer from the sign problem that makes quantum Monte Carlo methods ineffective. The PI is the inventor of the density matrix renormalization group (DMRG), one of the leading algorithms for simulating 1D systems. Within the last two decades, 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. This group is also the creator of ITensor, a widely used software library for carrying out DMRG and tensor network calculations, and development of ITensor will continue in this project.These simulation techniques have improved rapidly, and are now enabling a much better and deeper understanding of the 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. Recent improvments include better dynamics and better finite temperature treatments, for example, using the minimally entangled typical thermal state algorithm. To improve DMRG methods on molecules and realistic treatments of solids, this project is continuing work on developing diagonal Hamiltonian representations stemming from highly local basis sets. These diagonal representations dramatically improve the efficiency of DMRG. 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 the scientific community to enable discoveries across many areas of science.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.