The study of interacting fermions is fundamentally important to a wide range of physics research, including fields as diverse as electronic structure theory of solids, strongly correlated electron physics, quantum chemistry, and the theory of nuclear matter. Among other applications, the understanding of high-temperature superconductors depends on these interactions. This project will develop a new computational method for the controlled approximate solution of interacting fermion models. The method combines Monte Carlo (MC) summation techniques with self-consistent high-order Feynman diagram expansions. The implementation of the MC diagram summation method poses major algorithmic and computational challenges in several distinct areas of computational science and, by its very nature, requires a multi-disciplinary approach.
Technically, the project will develop novel computational graph theory algorithms and employ them to achieve a computationally efficient representation, generation and classification of Feynman graph topologies. New MC updating, scoring and variance minimization approaches will be implemented to carry out the simultaneous stochastic summation over diagram topologies and over internal momentum-energy variables. For the two-particle calculation, a novel combination of Lanczos matrix inversion and MC techniques is used to achieve efficient solutions of the Bethe-Salpeter equations with the full high-order irreducible interaction vertex. The efficient parallel implementation of the MC code is achieved by software pipelining and ring message passing approaches. These parallel applications are supported by novel parallel run-time systems that provide dynamic performance optimization.