Toward solving the sign problem with path optimization method
Toward solving the sign problem with path optimization method
复制标题
用路径优化方法求解符号问题
DOI：
10.1103/physrevd.96.111501
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Akira Ohnishi
中科院分区：
文献类型：
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作者：
Yuto Mori;Kouji Kashiwa;Akira Ohnishi
我们提出了一种新的方法来规避符号的问题，其中的集成路径进行了优化，以控制符号的问题。我们给出了一个试验函数指定的集成路径在复平面上，并调整它优化的成本函数，代表的严重性的标志问题。我们称之为路径优化方法。该方法不需要求解Lefschetz-thimble方法中的梯度流，而将积分路径轮廓的构造归结为一个优化问题，可以应用多种有效的方法。在一个符号问题严重的简单模型中，证明了路径优化方法的有效性，解决了剩余符号问题，即使在全局符号问题严重的区域也能得到精确的结果.
We propose a new approach to circumvent the sign problem in which the integration path is optimized to control the sign problem. We give a trial function specifying the integration path in the complex plane and tune it to optimize the cost function which represents the seriousness of the sign problem. We call it the path optimization method. In this method, we do not need to solve the gradient flow required in the Lefschetz-thimble method and then the construction of the integration-path contour arrives at the optimization problem where several efficient methods can be applied. In a simple model with a serious sign problem, the path optimization method is demonstrated to work well; the residual sign problem is resolved and precise results can be obtained even in the region where the global sign problem is serious.