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

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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.