平均Padé逼近的解析延拓
Analytic continuation by averaging Padé approximants
摘要：
本文利用Padé逼近技术研究了格林函数和自能的不适定解析延拓问题。我们建议补救众所周知的问题的Padé逼近进行平均数的几个延续，通过独立地改变拟合输入点和Padé系数的数量。建议的方法，然后应用到几个测试用例，包括Sm和Pr原子的自能，格林函数的哈伯德模型的Bethe晶格和Halflion模型的纳米带，以及两个特殊的测试功能。详细分析了数值库对数值噪声的敏感性和对数值库精度的依赖性。本方法进行了比较，一些其他的技术，即非负最小二乘法，非负Tikhonov方法和最大熵方法，并表现出良好的选择的测试用例。即使当输入数据上的噪声增加到达到量子蒙特卡罗模拟的典型值时，该结论也成立。最后说明了两个相关的测试功能的算法来解决精细结构的能力。
英文摘要：
The ill-posed analytic continuation problem for Green's functions and self-energies is investigated by revisiting the Padé approximants technique. We propose to remedy the well-known problems of the Padé approximants by performing an average of several continuations, obtained by varying the number of fitted input points and Padé coefficients independently. The suggested approach is then applied to several test cases, including Sm and Pr atomic self-energies, the Green's functions of the Hubbard model for a Bethe lattice and of the Haldane model for a nano-ribbon, as well as two special test functions. The sensitivity to numerical noise and the dependence on the precision of the numerical libraries are analysed in detail. The present approach is compared to a number of other techniques, i.e. the non-negative least-square method, the non-negative Tikhonov method and the maximum entropy method, and is shown to perform well for the chosen test cases. This conclusion holds even when the noise on the input data is increased to reach values typical for quantum Monte Carlo simulations. The ability of the algorithm to resolve fine structures is finally illustrated for two relevant test functions.
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