Preliminary Material

Krivenko, Ekaterina Yahyaoui

doi:10.1163/9789004346406_001

Cited by 4 publications

(4 citation statements)

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“…An example of a work where off-diagonal elements of the impurity spectral function are calculated are the DFT+DMFT calculations of the two perovskites LaVO 3 arXiv:1705.08838v2 [cond-mat.str-el] 6 Nov 2017 and YVO 3 [31]. Additionally, a stochastic regularization method also suitable for off-diagonal elements has been proposed [32]. However, these methods cannot ensure important matrix properties, e.g., positive semidefiniteness and Hermiticity of the spectral function.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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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.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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“…One method combines the Bayesian theory with the maximum entropy approach (MaxEnt), which has been found to be an efficient method for analytical continuation. 4,5 Other regularizations are used in the singular value decomposition (SVD) 6,7 or stochastic regularization 8 methods. An alternative is provided by making a Padé approximation to the data as a function of imaginary frequency and then analytically continue the Padé expression to real frequencies.…”

Section: Introductionmentioning

confidence: 99%

Analytical continuation of imaginary axis data for optical conductivity

2010

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We compare different methods for performing analytical continuation of spectral data from the imaginary time or frequency axis to the real frequency axis for the optical conductivity σ(ω). We compare the maximum entropy (MaxEnt), singular value decomposition (SVD), sampling and Padé methods for analytical continuation. We also study two direct methods for obtaining σ(0). For the MaxEnt approach we focus on a recent modification. The data are split up in batches, a separate MaxEnt calculation is done for each batch and the results are averaged. For the problems studied here, we find that typically the SVD, sampling and modified MaxEnt methods give comparable accuracy, while the Padé approximation is usually less reliable.

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“…The authors thank Hugo Strand and Vladimir Antropov for inspiring discussions. We kindly thank Igor Krivenko for providing the solver for stochastic optimization method for analytical continuation [77][78][79] used to obtain the data shown in Fig. 1.…”

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confidence: 99%

Effective Heisenberg Model and Exchange Interaction for Strongly Correlated Systems

et al. 2018

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We consider the extended Hubbard model and introduce a corresponding Heisenberg-like problem written in terms of spin operators. The derived formalism is reminiscent of Anderson's idea of the effective exchange interaction and takes into account nonlocal correlation effects. The results for the exchange interaction and spin susceptibility in the magnetic phase are expressed in terms of single-particle quantities. This fact not only can be used for realistic calculations of multiband systems but also allows us to reconsider a general description of many-body effects in the most interesting physical regimes, where the physical properties of the system are dominated by collective (bosonic) fluctuations. In the strongly spin-polarized limit, when the local magnetic moment is well defined, the exchange interaction reduces to a standard expression of the density functional theory that has been successfully used in practical calculations of magnetic properties of real materials.

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Preliminary Material

Cited by 4 publications

References 0 publications

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

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

Analytical continuation of imaginary axis data for optical conductivity

Effective Heisenberg Model and Exchange Interaction for Strongly Correlated Systems

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