Chin. Phys. Lett.  2017, Vol. 34 Issue (7): 077102    DOI: 10.1088/0256-307X/34/7/077102
Analytic Continuation with Padé Decomposition
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
2University of Chinese Academy of Sciences, Beijing 100049
3Collaborative Innovation Center of Quantum Matter, Beijing 100190
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Xing-Jie Han, Hai-Jun Liao, Hai-Dong Xie et al  2017 Chin. Phys. Lett. 34 077102
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Abstract The ill-posed analytic continuation problem for Green's functions or self-energies can be carried out using the Padé 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 Padé decomposition approach to replace the Matsubara frequency summation by a Padé frequency summation, and high precision input data can be obtained to successfully perform the Padé analytic continuation.
Received: 11 April 2017      Published: 23 June 2017
PACS:  71.15.Dx (Computational methodology (Brillouin zone sampling, iterative diagonalization, pseudopotential construction))  
  02.70.Hm (Spectral methods)  
Fund: Supported by the National Natural Science Foundation of China under Grant Nos 11474331 and 11190024.
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Xing-Jie Han
Hai-Jun Liao
Hai-Dong Xie
Rui-Zhen Huang
Zi-Yang Meng
Tao Xiang
[1]Mahan G D 2000 Many Particle Physics (New York: Kluwer Academic/Plenum Publishers)
[2]Blankenbecler R, Scalapino D J and Sugar R L 1981 Phys. Rev. D 24 2278
[3]Hirsch J E 1983 Phys. Rev. B 28 4059(R)
[4]Jarrell M and Gubernatis J E 1996 Phys. Rep. 269 133
[5]Bergeron D and Tremblay A M S 2016 Phys. Rev. E 94 023303
[6]Goulko O, Mishchenko A S, Pollet L, Prokofév N and Svistunov B 2017 Phys. Rev. B 95 014102
[7]Creffield C E, Klepfish E G, Pike E R and Sarkar S 1995 Phys. Rev. Lett. 75 517
[8]Gunnarsson O, Haverkort M W and Sangiovanni G 2010 Phys. Rev. B 82 165125
[9]Beach K S D 2004 arXiv:cond-mat/0403055
[10]Sandvik A W 2016 Phys. Rev. E 94 063308
[11]Qin Y Q, Normand B, Sandvik A W and Meng Z Y 2017 Phys. Rev. Lett. 118 147207
[12]Vidberg H J and Serene J 1977 J. Low Temp. Phys. 29 179
[13]Beach K S D, Gooding R J and Marsiglio F 2000 Phys. Rev. B 61 5147
[14]Östlin A, Chioncel L and Vitos L 2012 Phys. Rev. B 86 235107
[15]Osolin Ž and Žitko R 2013 Phys. Rev. B 87 245135
[16]Schött J, Locht I L M, Lundin E, Grånäs O, Eriksson O and Marco I D 2016 Phys. Rev. B 93 075104
[17]Ozaki T 2007 Phys. Rev. B 75 035123
[18]Croy A and Saalmann U 2009 Phys. Rev. B 80 073102
[19]Hu J, Xu R X and Yan Y J 2010 J. Chem. Phys. 133 101106
[20]Hu J, Luo M, Jiang F, Xu R X and Yan Y J 2011 J. Chem. Phys. 134 244106
[21]Baym G and Mermin D 1961 J. Math. Phys. 2 232
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