Parallel loop cluster quantum Monte Carlo simulation of quantum magnets based on global union-find graph algorithm

A large-scale parallel loop cluster quantum Monte Carlo simulation is presented. On 24,576 nodes of the K computer, one loop cluster Monte Carlo update of the world-line configuration of the S = 1/2 antiferromagnetic Heisenberg chain with 2.6 x 10(6) spins at inverse temperature 3.1 x 10(5) is executed in about 8.62 s, in which global union-find cluster identification on a graph of about 1.1 trillion vertices and edges is performed. By combining the nonlocal global updates and the large-scale parallelization, we have virtually achieved about 10(13)-fold speed-up from the conventional local update Monte Carlo simulation performed on a single core. We have estimated successfully the antiferromagnetic correlation length and the magnitude of the first excitation gap of the S = 4 antiferromagnetic Heisenberg chain for the first time as xi = 1.040(7) x 10(4) and Delta = 7.99(5) x 10(-4), respectively. (C) 2019 Elsevier B.V. All rights reserved.