Optimization of Reordering Procedures in HOTRG for Distributed Parallel Computing

Higher-order tensor renormalization group (HOTRG) is a coarse-graining algorithm for approximating the partition function in the field of elementary particle physics using a tensor network. Coarse-graining in HOTRG comprises an approximation step and a contraction step, and the contraction step is performed with tensor reorderings and matrix products. In this paper, we introduce a naive parallel implementation of HOTRG and propose optimal reordering procedures for a three-dimensional (3D) classical cubic lattice Ising model. Numerical experiments on the K computer show that the elapsed time of the proposed procedure is 6.88 times faster than the naive one for the reorderings.