Analytic Continuation with Pade Decomposition

The ill-posed analytic continuation problem for Green＇s functions or self-energies can be carried out using the Pade rational polynomial approximation. However, to extract accurate results from this approximation, high precision input data of the Matsubara Green function are needed. The calculation...

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Bibliographic Details
Published inChinese physics letters Vol. 34; no. 7; pp. 203 - 206
Main Author 韩兴杰 廖海军 谢海东 黄瑞珍 孟子杨 向涛
Format Journal Article
LanguageEnglish
Published 01.06.2017
Subjects
Green函数
分解
收敛速度
有理多项式
格林函数
解析延拓
输入数据
高精度
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ISSN0256-307X
1741-3540
DOI10.1088/0256-307X/34/7/077102

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Summary:The ill-posed analytic continuation problem for Green＇s functions or self-energies can be carried out using the Pade rational polynomial approximation. However, to extract accurate results from this approximation, high precision input data of the Matsubara Green function are needed. The calculation of the Matsubara Green function generally involves a Matsubara frequency summation, which cannot be evaluated analytically. Numerical summation is requisite but it converges slowly with the increase of the Matsubara frequency. Here we show that this slow convergence problem can be significantly improved by utilizing the Pade decomposition approach to replace the Matsubara frequency summation by a Pade frequency summation, and high precision input data can be obtained to successfully perform the Pade analytic continuation.
Bibliography:11-1959/O4
The ill-posed analytic continuation problem for Green＇s functions or self-energies can be carried out using the Pade rational polynomial approximation. However, to extract accurate results from this approximation, high precision input data of the Matsubara Green function are needed. The calculation of the Matsubara Green function generally involves a Matsubara frequency summation, which cannot be evaluated analytically. Numerical summation is requisite but it converges slowly with the increase of the Matsubara frequency. Here we show that this slow convergence problem can be significantly improved by utilizing the Pade decomposition approach to replace the Matsubara frequency summation by a Pade frequency summation, and high precision input data can be obtained to successfully perform the Pade analytic continuation.
Xing-Jie Han1,2, Hai-Jun Liao1,2, Hai-Dong Xie1,2, Rui-Zhen Huang1,2 Zi-Yang Meng1,2, Tao Xiang1,,2,3（ 1Institute of Physics, Chinese Academy of Sciences, Beijing 100190 2 University of Chinese Academy of Sciences, Beijing 100049 3 Collaborative Innovation Center of Quantum Matter, Beijing 100190）
ISSN:0256-307X
1741-3540
DOI:10.1088/0256-307X/34/7/077102