Highly Parallel Solver for Multi-scale Parquet Quantum Modeling of Strongly Correlated Materials

Abstract

The parquet formalism to calculate the two-particle Green’s functions of large systems requires the solution of a large, sparse, complex system of quadratic equations. If Nf Matsubara frequencies are used for a system of size Nc , and Newton’s method is used to solve the nonlinear system, the Jacobian system has O(8Nt^3 ) variables and O(40Nt^4 ) complex entries where Nt = Nc Nf . For Nt = 1024, the nonlinear system has over 8.5 billion degrees of freedom and the sparse Jacobian will require over 351 TBytes of memory. The Jacobian is very expensive to store but the matrix-vector products can be computed directly. We are developing a highly scalable parallel solver that uses both OpenMP and MPI to exploit the multicore nodes. We present initial scalability results on the Cray XT5 that suggests the code can be scaled to solve larger problems with Nt ≥ 1024.