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 $2.6 \times 10^6$ 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.Comment: 16 pages, 9 figure

DSQSS: Discrete Space Quantum Systems Solver

The Discrete Space Quantum Systems Solver (DSQSS) is a program package for solving quantum many-body problems defined on lattices. The DSQSS is based on the quantum Monte Carlo method in Feynman's path integral representation and covers a broad range of problems using flexible input files that define arbitrary unit cells in arbitrary dimensions and arbitrary matrix elements representing the interactions among an arbitrary number of degrees of freedom. Finite temperature calculations of quantum spin and the Bose- Hubbard models can be performed by specifying parameters such as the number of dimensions, the lattice size, coupling constants, and temperature. The present paper details the use of DSQSS and presents a number of applications thereof.Comment: 13 pages, 6 figures, accepted manuscrip