The International Conference for High Performance Computing, Networking, Storage and Analysis
Loop Cluster Monte Carlo Simulation of Quantum Magnets Based on Global Union-Find Algorithm.
Authors: Synge Todo (University of Tokyo), Haruhiko Matsuo (Research Organization for Information Science and Technology), Hideyuki Shitara (Fujitsu Limited)
Abstract: A large-scale parallel loop cluster algorithm quantum Monte Carlo simulation on the K computer is presented. On 24,576 nodes of the K computer, one Monte Carlo update of the world-line configuration of the spin-1/2 antiferromagnetic Heisenberg chain with 2,621,440 spins at inverse temperature 310,690 is executed in about 8.62 seconds, 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 on the K computer, we have virtually achieved about 10^17-fold speed-up. By using the highly parallelized quantum Monte Carlo algorithm, we have estimated successfully the magnitude of the first excitation gap and the antiferromagnetic correlation length of the spin-4antiferromagnetic Heisenberg chain for the first time as 0.000799 +/- 0.000005 and 10,400 +/- respectively.