Efficient parallel implementation of Bose Hubbard model: Exact numerical ground states and dynamics of gaseous Bose–Einstein condensates

We present a parallel implementation of the Bose Hubbard model, using imaginary time propagation to find the lowest quantum eigenstate and real time propagation for simulation of quantum dynamics. Scaling issues, performance of sparse matrix–vector multiplication, and a parallel algorithm for determining nonzero matrix elements are described. Implementation of imaginary time propagation yields an O(N) linear convergence on a single processor and slightly better than ideal performance on up to 160 processors for a particular problem size. The determination of the nonzero matrix elements is intractable using sequential non-optimized techniques for large problem sizes. Thus, we discuss a parallel algorithm that takes advantage of the intrinsic structural characteristics of the Fock-space matrix representation of the Bose Hubbard Hamiltonian and utilizes a parallel implementation of a Fock state look up table to make this task solvable within reasonable timeframes. Our parallel algorithm demonstrates near ideal scaling on thousand of processors. We include results for a matrix 22.6 million square, with 202 million nonzero elements, utilizing 2048 processors.