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Instructive discussion of an effective block algorithm for baryon-baryon correlators

We describe an approach for the efficient calculation of a large number of four-point correlation functions for various baryon-baryon (BB) channels, which are the primary quantities for studying the nuclear and hyperonic nuclear forces from lattice quantum chromodynamics. Using the four-point correlation function of a proton-$Λ$ system as a specific example, we discuss how an effective block algorithm significantly reduces the number of iterations. The effective block algorithm is applied to calculate 52 channels of the four-point correlation functions from nucleon$-$nucleon to $Ξ-Ξ$, in order to study the complete set of isospin symmetric BB interactions. The elapsed times measured for hybrid parallel computation on BlueGene/Q demonstrate that the performance of the present algorithm is reasonable for various combinations of the number of OpenMP threads and the number of MPI nodes. The numerical results are compared with the results obtained using the unified contraction algorithm for all computed sites of the 52 four-point correlators.