Worldvolume approach to the tempered Lefschetz thimble method
Worldvolume approach to the tempered Lefschetz thimble method
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DOI：
10.1093/ptep/ptab010
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发表时间：
2020-12
影响因子：
3.5
通讯作者：
M. Fukuma;N. Matsumoto
中科院分区：
文献类型：
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作者：
M. Fukuma;N. Matsumoto
作为对数值标志问题的解决方案，我们提出了一种新型的杂化蒙特卡洛算法，其中分子动力学是在连续的一组整合的整合表面上进行的，这是由抗黑晶梯度流动的（“整合表面的世界vollume”）在此新的TLTM中，在此新的TLTM中，钢化级别的弹簧级别方法（TLTM）的扩展简单地解决了符号和多模式问题。算法，不再需要计算梯度流的雅各布式生成配置，并且只需要在测量时评估其相位，即可证明该算法有效，我们将算法应用于手性随机矩阵模型复杂的Langevin方法已知不起作用。
As a solution towards the numerical sign problem, we propose a novel hybrid Monte Carlo algorithm, in which molecular dynamics is performed on a continuum set of integration surfaces foliated by the antiholomorphic gradient flow (“the worldvolume of an integration surface”). This is an extension of the tempered Lefschetz thimble method (TLTM) and solves the sign and multimodal problems simultaneously, as the original TLTM does. Furthermore, in this new algorithm, one no longer needs to compute the Jacobian of the gradient flow in generating a configuration, and only needs to evaluate its phase upon measurement. To demonstrate that this algorithm works correctly, we apply the algorithm to a chiral random matrix model, for which the complex Langevin method is known not to work.