Stochastic pole expansion method for analytic continuation of the Green's function
被引:4
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作者:
Huang, Li
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机构:
Sci & Technol Surface Phys & Chem Lab, POB 9-35, Jiangyou 621908, Peoples R ChinaSci & Technol Surface Phys & Chem Lab, POB 9-35, Jiangyou 621908, Peoples R China
Huang, Li
[1
]
Liang, Shuang
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机构:
Chinese Acad Sci, Inst Phys, Beijing 100190, Peoples R China
Yangtze River Delta Phys Res Ctr, Liyang 213300, Jiangsu, Peoples R ChinaSci & Technol Surface Phys & Chem Lab, POB 9-35, Jiangyou 621908, Peoples R China
Liang, Shuang
[2
,3
]
机构:
[1] Sci & Technol Surface Phys & Chem Lab, POB 9-35, Jiangyou 621908, Peoples R China
[2] Chinese Acad Sci, Inst Phys, Beijing 100190, Peoples R China
[3] Yangtze River Delta Phys Res Ctr, Liyang 213300, Jiangsu, Peoples R China
In this paper, we propose an analytic continuation method to extract real-frequency spectral functions from imaginary-frequency Green's functions of quantum many-body systems. This method is based on the pole representation of Matsubara Green's function and a stochastic sampling procedure is utilized to optimize the amplitudes and locations of poles. In order to capture narrow peaks and sharp band edges in the spectral functions, a constrained sampling algorithm and a self-adaptive sampling algorithm are developed. To demonstrate the usefulness and performance of this method, we at first apply it to study the spectral functions of representative fermionic and bosonic correlators. Then we employ this method to tackle the analytic continuation problems of matrix-valued Green's functions. The synthetic Green's functions, as well as realistic correlation functions from finite-temperature quantum many-body calculations, are used as input. The benchmark results demonstrate that this method is capable of reproducing most of the key characteristics in the spectral functions. The sharp, smooth, and multipeak features in both low-and high-frequency regions of spectral functions could be accurately resolved, which overcomes one of the main limitations of the traditional maximum entropy method. More importantly, it exhibits excellent robustness with respect to noisy and incomplete input data. The causality of spectral function is always satisfied even in the presence of sizable noises. As a by-product, this method could derive a fitting formula for the Matsubara data, which provides a compact approximation to the many-body Green's functions. Hence, we expect that this method could become a pivotal workhorse for numerically analytic continuation and be broadly useful in many applications.
机构:
Sci & Technol Surface Phys & Chem Lab, POB 9-35, Jiangyou 621908, Peoples R ChinaSci & Technol Surface Phys & Chem Lab, POB 9-35, Jiangyou 621908, Peoples R China
Huang, Li
Liang, Shuang
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机构:
Chinese Acad Sci, Inst Phys, Beijing 100190, Peoples R China
Yangtze River Delta Phys Res Ctr, Liyang 213300, Jiangsu, Peoples R ChinaSci & Technol Surface Phys & Chem Lab, POB 9-35, Jiangyou 621908, Peoples R China
机构:
Guangdong Ocean Univ, Coll Sci, Zhanjiang 524088, Peoples R China
Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R ChinaGuangdong Ocean Univ, Coll Sci, Zhanjiang 524088, Peoples R China
机构:
Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USAUniv Calif Berkeley, Dept Math, Berkeley, CA 94720 USA
Huang, Zhen
Gull, Emanuel
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Univ Michigan, Dept Phys, Ann Arbor, MI 48109 USAUniv Calif Berkeley, Dept Math, Berkeley, CA 94720 USA
Gull, Emanuel
Lin, Lin
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机构:
Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA
Lawrence Berkeley Natl Lab, Appl Math & Computat Res Div, Berkeley, CA 94720 USAUniv Calif Berkeley, Dept Math, Berkeley, CA 94720 USA