Implementation of the HMC algorithm on the tempered Lefschetz thimble method
Implementation of the HMC algorithm on the tempered Lefschetz thimble method
复制标题
HMC算法在回火Lefschetz顶针法上的实现
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
N. Umeda
中科院分区：
文献类型：
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作者：
M. Fukuma;N. Matsumoto;N. Umeda
回火Lefschetz thimble方法（TLTM）是一种求解数值符号问题的并行回火算法，通过反全纯梯度流对系统进行回火以同时驯服符号问题和遍历问题。在本文中，我们针对每个流动表面上的跃迁实现了混合蒙特卡罗（HMC）算法，期望这种在TLTM上的实现将为未来包括费米子在内的大规模系统的计算提供一个有用的框架。虽然使用HMC在莱夫谢茨顶针方法已被提出到目前为止，我们在这里的关键成就是，HMC是在TLTM上实现，以便在TLTM的并行回火算法，特别是通过开发一种算法来处理零的费米子行列式的过程中的分子动力学过程。我们确认，该算法的工作原理正确地将其应用到一个小格子上的哈伯德模型的符号问题，TLTM是已知的工作与大都会算法。我们表明，使用HMC显着减少了自相关时间与更少的计算时间相比，大都会算法。
The tempered Lefschetz thimble method (TLTM) is a parallel-tempering algorithm towards solving the numerical sign problem, where the system is tempered by the antiholomorphic gradient flow to tame both the sign and ergodicity problems simultaneously. In this paper, we implement the hybrid Monte Carlo (HMC) algorithm for transitions on each flowed surface, expecting that this implementation on TLTM will give a useful framework for future computations of large-scale systems including fermions. Although the use of HMC in Lefschetz thimble methods has been proposed so far, our crucial achievement here is that HMC is implemented on TLTM so as to work within the parallel-tempering algorithm in TLTM, especially by developing an algorithm to handle zeros of fermion determinants in the course of the molecular-dynamics process. We confirm that the algorithm works correctly by applying it to the sign problem of the Hubbard model on a small lattice, for which the TLTM is known to work with the Metropolis algorithm. We show that the use of HMC significantly reduces the autocorrelation times with less computational times compared to the Metropolis algorithm.
DOI：
10.1088/1742-6596/706/2/022004
发表时间：
2015-12
期刊：
Journal of Physics: Conference Series
影响因子：
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作者：
G. Aarts
通讯作者：
G. Aarts