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Toward large-scale Hybrid Monte Carlo simulations of the Hubbard model on graphics processing units

机译:在图形处理单元上进行Hubbard模型的大规模混合Monte Carlo模拟

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摘要

One of the most efficient non-perturbative methods for the calculation of thermal properties of quantum systems is the Hybrid Monte Carlo algorithm, as evidenced by its use in large-scale lattice quantum chromodynamics calculations. The performance of this algorithm is determined by the speed at which the fermion operator is applied to a given vector, as it is the central operation in the preconditioned conjugate gradient iteration. We study a simple implementation of these operations for the fermion matrix of the Hubbard model in d+1 spacetime dimensions, and report a performance comparison between a 2.66 GHz Intel Xeon E5430 CPU and an NVIDIA Tesla C1060 GPU using double-precision arithmetic. We find speedup factors ranging between 30 and 350 for d=1, and in excess of 40 for d=3. We argue that such speedups are of considerable impact for large-scale simulational studies of quantum many-body systems.
机译:混合蒙特卡罗算法是计算量子系统热性质的最有效的非扰动方法之一,这种方法在大规模晶格量子色动力学计算中得到了证明。该算法的性能由费米子算子应用于给定向量的速度决定,因为它是预处理共轭梯度迭代中的中心运算。我们研究了在d + 1时空维度上对Hubbard模型的费米子矩阵的这些操作的简单实现,并报告了使用双精度算法的2.66 GHz Intel Xeon E5430 CPU和NVIDIA Tesla C1060 GPU之间的性能比较。对于d = 1,我们发现加速因子在30到350之间,而对于d = 3,加速因子超过40。我们认为,这种加速对于量子多体系统的大规模仿真研究具有相当大的影响。

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