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.

中文翻译：

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回火 Lefschetz 顶针法的 Worldvolume 方法

作为数字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，其中分子动力学是在由反全纯梯度流（“积分表面的世界体积”）形成的积分表面的连续集上执行的。这是回火 Lefschetz 顶针法 (TLTM) 的扩展，并与原始 TLTM 一样同时解决符号和多模态问题。此外，在这种新算法中，在生成配置时不再需要计算梯度流的雅可比，只需在测量时评估其相位。为了证明该算法正确工作，我们将该算法应用于手性随机矩阵模型，已知复杂的 Langevin 方法对其不起作用。