DMRG Studies of Frustrated and Doped Systems

该奖项支持理论和计算研究以及教育，以促进对具有许多相互作用粒子（特别是电子）的量子力学系统的理解。开发新的算法和软件来求解描述许多相互作用成分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突出的一个，密度矩阵重整化群（DMRG），并继续开发ITensor，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，一个大型国际科学家小组将DMRG扩展到张量网络，这是一个新的领域，应用范围从化学到黑洞物理学和引力量子理论。PI目前工作的重点是了解高温超导性和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性，这是一种电子的合作量子态，具有有趣的和技术上有用的特性，能够在它们之间不损失的情况下导电。大多数已知的超导体在接近绝对零度的温度下表现出超导性。高温超导体在氮变成液体的温度以上表现出超导性。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在室温和普通条件下表现出超导性的材料。改进分子的量子处理是量子计算机的主要潜在应用之一，可能会改进药物设计和能源应用材料。目前的工作重点是相同的发展，但使用当前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。ITensor软件库的进一步发展使得DMRG和张量网络方法对科学界有用，可以在许多科学领域中发现新的发现。技术概述该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，使这些模拟。这项工作的主要应用是掺杂费米子系统（如高温超导体）和受抑自旋系统，这些系统遭受使量子蒙特卡罗方法无效的符号问题。 PI是密度矩阵重整化群（DMRG）的发明者，这是模拟1D系统的领先算法之一。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包含了张量网络的许多想法。 该小组也是ITensor的创建者，ITensor是一个广泛使用的软件库，用于进行DMRG和张量网络计算，ITensor的开发将在本项目中继续进行。这些模拟技术已经迅速改进，现在能够更好和更深入地了解高温超导体，特别是条纹和其他超导非均匀性之间的竞争，以及赝隙相的性质。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。 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，使用最小纠缠的典型热态算法。为了改进分子的DMRG方法和固体的现实处理，该项目正在继续开发源自高度局部基组的对角哈密顿表示。 这些对角表示极大地提高了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。ITensor软件库的进一步发展使DMRG和张量网络方法对科学界可用并有用，从而使许多科学领域的发现成为可能。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 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.