Project NSF ITR

Project description

The objective of this project is to combine Monte Carlo summation techniques with self-consistent high-order Feynman diagram expansions into an efficient tool for the controlled approximate solution of interacting fermion models. The implementation of this MC diagram summation method poses major algorithmic and computational challenges in several, quite distinct areas of computational science and, by its very nature, dictates a multi-disciplinary approach.

Specifically, the underlying expansion formalism and its implementation require self-consistent, conserving approximation schemes, derived from diagrammatic quantum many-body theory. Novel algorithmic approaches in computational graph theory will be needed to achieve computationally efficient representation, generation and classification of Feynman graph topologies. The simultaneous stochastic summation over diagram topologies and over internal momentum-energy variables requires novel MC updating and scoring approaches as well as major efforts to achieve variance minimization . And, last but not least, the efficient, scalable and portable parallel implementation of the MC code poses unique challenges in parallel computing, requiring new parallelization strategies and the development of novel parallel run-time systems.

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Center for Simulational Physics

Dep. of Physics and Astronomy