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 $2.6\times 10^6$ spins at inverse temperature $3.1\times 10^5$ 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, 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 $\xi =1.040(7)\times 10^4$ and $\Delta =7.99(5)\times 10^{-4}$, respectively.

16 pages, 9 figures

References in corpus (4)

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• Thermal Phase Transition of Generalized Heisenberg Models for SU(N) Spins on Square and Honeycomb Lattices
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• Physics of integer spin antiferromagnetic chains : Haldane gaps and edge states
• DSQSS: Discrete Space Quantum Systems Solver
• Haldane Gaps of Large-S Heisenberg Antiferromagnetic Chains and Asymptotic Behavior
• Asymptotic Freedom and Large Spin Antiferromagnetic Chains
• Extraordinary magnetic response of an anisotropic 2D antiferromagnet via site-dilution