Maximum entropy formalism for the analytic continuation of matrix-valued Green’s functions

Gernot J. Kraberger, Robert Triebl, Manuel Zingl, Markus Aichhorn

Publikation: Beitrag in einer FachzeitschriftArtikelBegutachtung

Abstract

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 LaTiO3, where off-diagonal matrix elements in the Green's function appear due to the distorted crystal structure.
Originalspracheenglisch
Aufsatznummer155128
Seitenumfang14
FachzeitschriftPhysical Review B
Jahrgang96
DOIs
PublikationsstatusVeröffentlicht - 2017

Fields of Expertise

  • Advanced Materials Science

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)
  • Theoretical

Kooperationen

  • NAWI Graz

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