adapol：用于量子多体物理的自适应极点拟合

中文摘要 AI 辅助

我们描述了adapol，一个用于通过具有实极点位置和矩阵值残差的简单极点紧凑和来拟合Matsubara格林函数、自能和杂化函数的Python包。这一极点拟合步骤出现在许多情境中，包括基于精确对角化、微扰理论和张量网络的量子杂质求解器的杂化拟合，现有极点展开（如离散Lehmann表示）的压缩，基于离散极点表示的图解方法，以及Matsubara格林函数的解析延拓。adapol使用AAA有理逼近算法的修改版本来估计极点位置，并使用非凸优化来细化它们。该过程以黑盒且对噪声鲁棒的方式产生准确且紧凑的拟合。adapol提供了一个简单、自包含的接口，附有广泛的文档和示例，以及与TRIQS包的接口。

英文摘要

We describe adapol, a Python package for fitting Matsubara Green's functions, self-energies, and hybridization functions by a compact sum of simple poles with real pole locations and matrix-valued residues. This pole-fitting step arises in many contexts, including hybridization fitting for quantum impurity solvers based on exact diagonalization, perturbation theory, and tensor networks, the compression of existing pole expansions such as the discrete Lehmann representation, diagrammatic methods based on discrete pole representations, and the analytic continuation of Matsubara Green's functions. adapol uses a modified version of the AAA rational approximation algorithm to estimate pole locations, and non-convex optimization to refine them. This procedure yields accurate and compact fits in a black-box and noise-robust manner. adapol provides a simple, self-contained interface with extensive documentation and examples, as well as an interface to the TRIQS package.

发表机构

• Center for Computational Quantum Physics, Flatiron Institute（Flatiron Institute 计算量子物理中心）
• Center for Computational Mathematics, Flatiron Institute（Flatiron Institute 计算数学中心）
• Department of Mathematics, University of California, Berkeley（加州大学伯克利分校数学系）
• Department of Computing and Mathematical Sciences, California Institute of Technology（加州理工学院计算与数学科学系）
• Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室应用数学与计算研究部）
• School of Science and Technology, Örebro University（Örebro University 科学与技术学院）

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