Worldvolume approach to the tempered Lefschetz thimble method

M. Fukuma, N. Matsumoto
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引用次数: 27

Abstract

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.
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调质Lefschetz顶针法的世界体积方法
作为数值符号问题的解决方案,我们提出了一种新的混合蒙特卡罗算法,其中分子动力学在由反全纯梯度流(“积分曲面的世界体积”)分叶的积分曲面连续集上进行。这是对缓变Lefschetz顶针法(TLTM)的扩展,与原TLTM一样同时解决符号和多模态问题。此外,在该算法中,不再需要在生成构型时计算梯度流的雅可比矩阵,只需要在测量时计算其相位。为了证明该算法正确工作,我们将该算法应用于一个已知复杂朗之万方法无效的手性随机矩阵模型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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