利用路径优化方法规避了具有排斥矢量型相互作用的PNJL模型中的模型符号问题

A. Ohnishi, Y. Mori, K. Kashiwa
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引用次数: 1

摘要

利用路径优化方法讨论了具有排斥矢量型相互作用的Polyakov环扩展Nambu—Jona-Lasinio模型中的符号问题。在该模型中,Polyakov环和矢量型相互作用都会引起模型符号问题,并且在平均场处理中也使用了几种处方。在路径优化方法中,对积分变量进行复化,对积分路径(流形)进行优化,以避免符号问题,即提高平均相位因子。在均匀场分析范围内,采用前馈神经网络对路径进行优化。我们发现在之前的工作中采用的假设$\mathrm{Re}\,A_8 \simeq 0$和$\mathrm{Re}\,\omega \simeq 0$可以通过在优化路径上采样的蒙特卡罗构型来证明。并推导出最优路径的欧拉-拉格朗日方程。在统计权值较大的区域,Euler-Lagrange方程的解和变分优化路径是一致的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Evading the model sign problem in the PNJL model with repulsive vector-type interaction via path optimization
We discuss the sign problem in the Polyakov loop extended Nambu--Jona-Lasinio model with repulsive vector-type interaction by using the path optimization method. In this model, both of the Polyakov loop and the vector-type interaction cause the model sign problem, and several prescriptions have been utilized even in the mean field treatment. In the path optimization method, integration variables are complexified and the integration path (manifold) is optimized to evade the sign problem, or equivalently to enhance the average phase factor. Within the homogeneous field ansatz, the path is optimized by using the feedforward neural network. We find that the assumptions adopted in previous works, $\mathrm{Re}\,A_8 \simeq 0$ and $\mathrm{Re}\,\omega \simeq 0$, can be justified from the Monte-Carlo configurations sampled on the optimized path. We also derive the Euler-Lagrange equation for the optimal path to satisfy. The two optimized paths, the solution of the Euler-Lagrange equation and the variationally optimized path, agree with each other in the region with large statistical weight.
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