论文标题
通过投影，极估计和半芬矿放松，绿色功能的强大分析延续
Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation
论文作者
论文摘要
格林的fermions功能由矩阵值Herglotz-Nevanlinna函数描述。由于分析延续在根本上是一个不足的问题，因此基质值为HERGLOTZ-NEVANLINNA结构描述的因果空间可能有助于提高准确性和增强噪声方面的鲁棒性。我们展示了一个三管齐下的程序，用于强大的分析延续，称为PES：（1）数据投影到因果空间中。 （2）极点位置的估计。 （3）在因果空间内的半决赛松弛。我们将PES的性能与最近开发的Nevanlinna和Carathéodory延续方法进行了比较，并发现PES在存在噪声的情况下更强大，并且不需要使用扩展的精确算术。我们还证明了因果投影改善了Nevanlinna和Carathéodory方法的性能。 PES方法概括为骨气响应函数，尚未开发Nevanlinna和Carathéodory延续方法。它在研究固体中的分子和带结构的研究中出现在具有鲜明特征的光谱方面特别有用。
Green's functions of fermions are described by matrix-valued Herglotz-Nevanlinna functions. Since analytic continuation is fundamentally an ill-posed problem, the causal space described by the matrix-valued Herglotz-Nevanlinna structure can be instrumental in improving the accuracy and in enhancing the robustness with respect to noise. We demonstrate a three-pronged procedure for robust analytic continuation called PES: (1) Projection of data to the causal space. (2) Estimation of pole locations. (3) Semidefinite relaxation within the causal space. We compare the performance of PES with the recently developed Nevanlinna and Carathéodory continuation methods and find that PES is more robust in the presence of noise and does not require the usage of extended precision arithmetics. We also demonstrate that a causal projection improves the performance of the Nevanlinna and Carathéodory methods. The PES method is generalized to bosonic response functions, for which the Nevanlinna and Carathéodory continuation methods have not yet been developed. It is particularly useful for studying spectra with sharp features, as they occur in the study of molecules and band structures in solids.
