Maximum entropy formalism for the analytic continuation of matrix-valued Green's functions
| Autor: | Robert Triebl, Manuel Zingl, Gernot J. Kraberger, Markus Aichhorn |
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| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Condensed Matter - Materials Science
Strongly Correlated Electrons (cond-mat.str-el) Analytic continuation Mathematical properties Materials Science (cond-mat.mtrl-sci) FOS: Physical sciences Maximum entropy formalism Computational Physics (physics.comp-ph) 16. Peace & justice 01 natural sciences Bayesian probability theory 010305 fluids & plasmas Green S chemistry.chemical_compound Condensed Matter - Strongly Correlated Electrons Test case chemistry Full matrix 0103 physical sciences Applied mathematics Entropy (information theory) 010306 general physics Physics - Computational Physics Mathematics |
| Popis: | We present a generalization of the maximum entropy method to the analytic continuation of matrix-valued Green's functions. To treat off-diagonal elements correctly based on Bayesian probability theory, the entropy term has to be extended for spectral functions that are possibly negative in some frequency ranges. In that way, all matrix elements of the Green's function matrix can be analytically continued; we introduce a computationally cheap element-wise method for this purpose. However, this method cannot ensure important constraints on the mathematical properties of the resulting spectral functions, namely positive semidefiniteness and Hermiticity. To improve on this, we present a full matrix formalism, where all matrix elements are treated simultaneously. We show the capabilities of these methods using insulating and metallic dynamical mean-field theory (DMFT) Green's functions as test cases. Finally, we apply the methods to realistic material calculations for LaTiO$_3$, where off-diagonal matrix elements in the Green's function appear due to the distorted crystal structure. 15 pages, 7 figures |
| Databáze: | OpenAIRE |
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