Parallel tempering algorithm for integration over Lefschetz thimbles
Parallel tempering algorithm for integration over Lefschetz thimbles
复制标题
用于 Lefschetz 顶针积分的并行回火算法
DOI：
10.1093/ptep/ptx081
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发表时间：
2017
影响因子：
3.5
通讯作者：
Masafumi Fukuma and Naoya Umeda
中科院分区：
文献类型：
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作者：
S.Urakawa;K.Ohtsuka;S.Abe;D.Kinoshita;H.Hanayama;T.Miyaji;S.Okumura;K.Ayani;S.Maeno;D.Kuroda;A.Fukui;N.Narita;G.L.Hashimoto;Y.Sakurai;S.Nakamura;J.Takahashi;T.Tanigawa;O.Burhonov;K.Ergashev;T.Ito;F.Yoshida;M.Watanabe;M.Imai;K.Kurama;Masafumi Fukuma and Naoya Umeda
基于 Lefschetz 顶针积分的算法是解决复杂动作符号问题的一种很有前途的方法。然而，该算法在实际的蒙特卡罗计算中常常遇到困难，因为不同顶针之间的势垒无限高，配置空间不易探索。在本文中，我们建议使用反全纯梯度流的流动时间作为高度多峰分布的辅助变量。为了说明这一点，我们通过将流动时间作为回火参数来实现并行回火方法。在该算法中，我们可以将最大流动时间设置得足够大，使得符号问题消失，并且通过小流动时间的配置将两个单独的模式连接起来。为了证明该算法确实有效，我们研究了有限密度下的 (0 + 1) 维大规模 Thirring 模型，并表明我们的算法正确地再现了大流动时间（例如 T= 2）的分析结果。
The algorithm based on integration over Lefschetz thimbles is a promising method to resolve the sign problem for complex actions. However, this algorithm often meets a difficulty in actual Monte Carlo calculations because the configuration space is not easily explored due to the infinitely high potential barriers between different thimbles. In this paper, we propose to use the flow time of the antiholomorphic gradient flow as an auxiliary variable for the highly multimodal distribution. To illustrate this, we implement the parallel tempering method by taking the flow time as a tempering parameter. In this algorithm, we can take the maximum flow time to be sufficiently large such that the sign problem disappears there, and two separate modes are connected through configurations at small flow times. To exemplify that this algorithm does work, we investigate the (0 + 1)-dimensional massive Thirring model at finite density and show that our algorithm correctly reproduces the analytic results for large flow times such asT= 2.