We present a generalization of the maximum entropy method to the analyticcontinuation of matrix-valued Green's functions. To treat off-diagonal elementscorrectly based on Bayesian probability theory, the entropy term has to beextended for spectral functions that are possibly negative in some frequencyranges. In that way, all matrix elements of the Green's function matrix can beanalytically continued; we introduce a computationally cheap element-wisemethod for this purpose. However, this method cannot ensure importantconstraints on the mathematical properties of the resulting spectral functions,namely positive semidefiniteness and Hermiticity. To improve on this, wepresent a full matrix formalism, where all matrix elements are treatedsimultaneously. We show the capabilities of these methods using insulating andmetallic 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 thedistorted crystal structure.
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