AI 中文总结
研究将路径优化方法用于斯蒂芬诺夫模型和手征随机矩阵模型减轻符号问题，在高化学势下该方法成功改善斯蒂芬诺夫模型平均相位因子，低化学势下则失败，其相位因子行为趋势与全局符号问题相关。
AI 中文摘要
路径优化方法应用于与量子色动力学（QCD）有若干共同特性的斯蒂芬诺夫模型和手征随机矩阵模型，以减轻由费米子行列式引起的符号问题。斯蒂芬诺夫模型是有限密度QCD的典型模型，手征随机矩阵模型代表具有银色火焰现象的理想系统。我们表明，路径优化在高化学势下成功改善了斯蒂芬诺夫模型中的平均相位因子，以减少的统计误差重现了分析结果。然而，它未能改善低化学势下斯蒂芬诺夫模型以及手征随机矩阵模型中的平均相位因子。相位因子行为的这种趋势似乎与全局符号问题密切相关。
英文摘要
The path optimization method is applied to the Stephanov model and the chiral random matrix model, both of which share several properties with QCD, to mitigate the sign problem caused by the fermion determinant. The Stephanov model serves as a prototypical model of finite-density QCD, while the chiral random matrix model represents an ideal system featuring the Silver Blaze phenomenon. We show that the path optimization successfully improves the average phase factor in the Stephanov model at high chemical potential, reproducing the analytical results with reduced statistical errors. However, it fails to improve the average phase factor in the Stephanov model at low chemical potential, as well as in the chiral random matrix model. This tendency in the phase factor behavior seems to be closely related to the global sign problem.
Comments7 pages, 6 figures
