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

Abstract

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 2.6×106 spins at inverse temperature 3.1×105 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 1013-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 ξ=1.040(7)×104 and Δ=7.99(5)×10−4, respectively.