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Models of fermions interacting with classical degrees of freedom are appliedto a large variety of systems in condensed matter physics. For this class ofmodels, Wei{\ss}e [Phys. Rev. Lett. {\bf 102}, 150604 (2009)] has recentlyproposed a very efficient numerical method, called O($N$) Green-Function-BasedMonte Carlo (GFMC) method, where a kernel polynomial expansion technique isused to avoid the full numerical diagonalization of the fermion Hamiltonianmatrix of size $N$, which usually costs O($N^3$) computational complexity.Motivated by this background, in this paper we apply the GFMC method to thedouble exchange model in three spatial dimensions. We mainly focus on theimplementation of GFMC method using both MPI on a CPU-based cluster andNvidia's Compute Unified Device Architecture (CUDA) programming techniques on aGPU-based (Graphics Processing Unit based) cluster. The time complexity of thealgorithm and the parallel implementation details on the clusters arediscussed. We also show the performance scaling for increasing Hamiltonianmatrix size and increasing number of nodes, respectively. The performanceevaluation indicates that for a $32^3$ Hamiltonian a single GPU shows higherperformance equivalent to more than 30 CPU cores parallelized using MPI.

A Study of Parallelizing O(N) Green-Function-Based Monte Carlo Method for Many Fermions Coupled with Classical Degrees of Freedom