Collaborative research: Development of efficient petascale algorithms for inhomogeneous quantum-mechanical systems

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。随着新型超级计算机的出现，这些计算机拥有数十万个处理器，运算速度接近每秒一千万亿次，许多甚至在几年前还无法解决的重大挑战科学问题可以得到解决。这个由物理学家和计算机科学家组成的团队将基于所谓的Lanczos方法开发新的计算算法，该方法涉及使用稀疏矩阵的幂乘以初始向量，从而找到大型稀疏矩阵的逆的对角线，并找到所有的特征值和特征向量。开发的代码将考虑到特定的内存寻址和访问问题，这些问题与试图在如此大的机器上有效地运行这些代码有关。这些可能在科学界广泛使用的数值算法将在本工作中应用于两个科学难题。第一个是描述放置在所谓的光学晶格上的超冷原子是如何以量子力学的方式相互作用的。在光学晶格中，原子沿着波纹状的“蛋盒状”表面运动。该团队将与该领域的一组世界领先的实验小组合作，解决与这些系统行为相关的一些理论和计算问题。这些问题本身就很困难，因为原子被放置在一个陷阱中，就像粒子坐在碗里一样，这使得现有的技术很难应用于这些系统。第二个问题是量子自旋玻璃的行为。玻璃态行为本身就是一个困难的问题，因为无序破坏了系统的周期性，使其具有挑战性。传统的方法，如量子蒙特卡罗模拟失败，由于自旋受挫的性质。我们的工作，基于高温级数展开的扩展，能够描述低温性质，将允许人们准确地探测这些迷人系统的基态性质，这些系统被认为是显示拓扑秩序或紧急合作行为。该团队还将研究与使用现代并行编程模型（如分区全局地址空间（PGAS），特别是UPC）相关的生产力权衡，以解决这类问题。根据本授权开发的通用数字代码将通过GNU公共许可证分发。该项目还将培养大规模科学计算领域的年轻研究人员。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).With the advent of new supercomputers that employ hundreds of thousands of processors and can compute at speeds approaching one quadrillion operations per second, many grand challenge science problems can be solved which were unsolvable even a few years ago. This team of physicists and computer scientists will develop new computational algorithms based on the so-called Lanczos method, which involves using powers of a sparse matrix multiplying an initial vector, that will find the diagonal of the inverse of large sparse matrices and will find all of the eigenvalues and eigenvectors. The codes that are developed will take into account the specific memory addressing and accessing issues associated with trying to run these codes efficiently on such large machines. These numerical algorithms, which are likely to have wide use within the scientific community, will be applied to two hard scientific problems in this work. The first is to describe how ultracold atoms placed on a so-called optical lattice, where the atoms move along a corrugated "egg-carton-like" surface, interact with each other quantum-mechanically. Working with a group of the world's leading experimental groups in this area, this team will solve a number of theoretical and computational problems related to the behavior of these systems. The problems are inherently difficult because the atoms are placed in a trap, like particles sitting in a bowl, which makes established techniques very difficult to employ on these systems. The second problem is the behavior of a quantum spin glass. Glassy behavior is an inherently difficult problem, because the disorder breaks the periodicity of the system, and makes it challenging to solve. Conventional methods like quantum Monte Carlo simulations fail due to the frustrated nature of the spins. Our work, based on an extension of high temperature series expansions to be able to describe low-temperature properties, will allow one to accurately probe the ground state properties of these fascinating systems which are believed to display either topological order or emergent cooperative behavior. The team will also investigate the productivity trade offs associated with the use of modern parallel programming models, such as the partitioned global address space (PGAS), particularly UPC, for this class of problems. The general purpose numerical codes developed under this grant will be distributed via the GNU public license. This project will also train younger researchers in large scale scientific computing.