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Analytical continuation of imaginary axis data using maximum entropy

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We study the maximum entropy (MaxEnt) approach for analytical continuation of spectral data from imaginary times to real frequencies. The total error is divided in a statistical error, due to the noise in the input data, and a systematic error, due to deviations of the default function, used in the...

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Main Authors: Gunnarsson, Olle (Author) , Haverkort, Maurits W. (Author) , Sangiovanni, Giorgio (Author)
Format: Article (Journal)
Language:English
Published: 9 April 2010
In: Physical review. B, Condensed matter and materials physics
Year: 2010, Volume: 81, Issue: 15, Pages: 155107
ISSN:1550-235X
DOI:10.1103/PhysRevB.81.155107
Online Access:Verlag, Volltext: http://dx.doi.org/10.1103/PhysRevB.81.155107
Verlag, Volltext: https://link.aps.org/doi/10.1103/PhysRevB.81.155107
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Author Notes:O. Gunnarsson, M.W. Haverkort, and G. Sangiovanni

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520 |a We study the maximum entropy (MaxEnt) approach for analytical continuation of spectral data from imaginary times to real frequencies. The total error is divided in a statistical error, due to the noise in the input data, and a systematic error, due to deviations of the default function, used in the MaxEnt approach, from the exact spectrum. We find that the MaxEnt approach in its classical formulation can lead to a nonoptimal balance between the two types of errors, leading to an unnecessary large statistical error. The statistical error can be reduced by splitting up the data in several batches, performing a MaxEnt calculation for each batch and averaging. This can outweigh an increase in the systematic error resulting from this approach. The output from the MaxEnt calculation can be used as a default function for a new MaxEnt calculation. Such iterations often lead to worse results due to an increase in the statistical error. By splitting up the data in batches, the statistical error is reduced and the increase resulting from iterations can be outweighed by a decrease in the systematic error. Finally we consider a linearized version to obtain a better understanding of the method. 
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