A comparison between methods of analytical continuation for bosonic functions

In this article we perform a critical assessment of different known methods for the analytical continuation of bosonic functions, namely the maximum entropy method, the non-negative least-square method, the non-negative Tikhonov method, the Pad\'e approximant method, and a stochastic sampling method. Three functions of different shape are investigated, corresponding to three physically relevant scenarios. They include a simple two-pole model function and two flavours of the non-interacting Hubbard model on a square lattice, i.e. a single-orbital metallic system and a two-orbitals insulating system. The effect of numerical noise in the input data on the analytical continuation is discussed in detail. Overall, the stochastic method by Mishchenko et al. [Phys. Rev. B \textbf{62}, 6317 (2000)] is shown to be the most reliable tool for input data whose numerical precision is not known. For high precision input data, this approach is slightly outperformed by the Pad\'e approximant method, which combines a good resolution power with a good numerical stability. Although none of the methods retrieves all features in the spectra in the presence of noise, our analysis provides a useful guideline for obtaining reliable information of the spectral function in cases of practical interest.Comment: 13 pages, 9 figure

Theoretical methods for the electronic structure and magnetism of strongly correlated materials

In this work we study the interesting physics of the rare earths, and the microscopic state after ultrafast magnetization dynamics in iron. Moreover, this work covers the development, examination and application of several methods used in solid state physics. The first and the last part are related to strongly correlated electrons. The second part is related to the field of ultrafast magnetization dynamics. In the first part we apply density functional theory plus dynamical mean field theory within the Hubbard I approximation to describe the interesting physics of the rare-earth metals. These elements are characterized by the localized nature of the 4f electrons and the itinerant character of the other valence electrons. We calculate a wide range of properties of the rare-earth metals and find a good correspondence with experimental data. We argue that this theory can be the basis of future investigations addressing rare-earth based materials in general. In the second part of this thesis we develop a model, based on statistical arguments, to predict the microscopic state after ultrafast magnetization dynamics in iron. We predict that the microscopic state after ultrafast demagnetization is qualitatively different from the state after ultrafast increase of magnetization. This prediction is supported by previously published spectra obtained in magneto-optical experiments. Our model makes it possible to compare the measured data to results that are calculated from microscopic properties. We also investigate the relation between the magnetic asymmetry and the magnetization. In the last part of this work we examine several methods of analytic continuation that are used in many-body physics to obtain physical quantities on real energies from either imaginary time or Matsubara frequency data. In particular, we improve the Padé approximant method of analytic continuation. We compare the reliability and performance of this and other methods for both one and two-particle Green's functions. We also investigate the advantages of implementing a method of analytic continuation based on stochastic sampling on a graphics processing unit (GPU)

A GPU code for analytic continuation through a sampling method

We here present a code for performing analytic continuation of fermionic Green’s functions and self-energies as well as bosonic susceptibilities on a graphics processing unit (GPU). The code is based on the sampling method introduced by Mishchenko et al. (2000), and is written for the widely used CUDA platform from NVidia. Detailed scaling tests are presented, for two different GPUs, in order to highlight the advantages of this code with respect to standard CPU computations. Finally, as an example of possible applications, we provide the analytic continuation of model Gaussian functions, as well as more realistic test cases from many-body physics

Analysis of the linear relationship between asymmetry and magnetic moment at the M edge of 3d transition metals

The magneto-optical response of Fe and Ni during ultrafast demagnetization is studied experimentally and theoretically. We have performed pump-probe experiments in the transverse magneto-optical Kerr effect (T-MOKE) geometry using photon energies that cover the M absorption edges of Fe and Ni between 40 and 72 eV. The magnetic asymmetry was obtained by forming the difference of reflected intensities obtained for two opposite orientations of the sample magnetization. Density functional theory (DFT) was used to calculate the magneto-optical response of different magnetic configurations, representing different types of excitations: long wavelength magnons, short wavelength magnons, and Stoner excitations. In the case of Fe, we find that the calculated asymmetry is strongly dependent on the specific type of magnetic excitation. Our modeling also reveals that during remagnetization Fe is, to a reasonable approximation, described by magnons, even though small nonlinear contributions could indicate some degree of Stoner excitations as well. In contrast, we find that the calculated asymmetry in Ni is rather insensitive to the type of magnetic excitations. However, there is a weak nonlinearity in the relation between asymmetry and the off-diagonal component of the dielectric tensor, which does not originate from the modifications of the electronic structure. Our experimental and theoretical results thus emphasize the need to consider a coupling between asymmetry and magnetization that may be more complex than a simple linear relationship. This insight is crucial for the microscopic interpretation of ultrafast magnetization experiments