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Comparison between methods of analytical continuation for bosonic functions
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
Radboud Univ Nijmegen, Inst Mol & Mat, Heyendaalseweg 135, NL-6525 AJ Nijmegen, Netherlands.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory. Radboud Univ Nijmegen, Inst Mol & Mat, Heyendaalseweg 135, NL-6525 AJ Nijmegen, Netherlands.
Radboud Univ Nijmegen, Inst Mol & Mat, Heyendaalseweg 135, NL-6525 AJ Nijmegen, Netherlands.
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2016 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 94, article id 245140Article in journal (Refereed) Published
Abstract [en]

In this article we perform a critical assessment of different known methods for the analytical con- tinuation 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 sam- pling method. Four functions of different shape are investigated, corresponding to four physically relevant scenarios. They include a simple two-pole model function, two flavours of the tight bind- ing model on a square lattice, i.e. a single-orbital metallic system and a two-orbitals insulating system, and the Hubbard dimer. 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 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. 

Place, publisher, year, edition, pages
2016. Vol. 94, article id 245140
Keywords [en]
Green's functions, analytical continuation
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:uu:diva-308693DOI: 10.1103/PhysRevB.94.245140ISI: 000391012400012OAI: oai:DiVA.org:uu-308693DiVA, id: diva2:1050645
Funder
Swedish Research CouncileSSENCE - An eScience CollaborationKnut and Alice Wallenberg FoundationEU, European Research Council, 338957 FEMTO/NANOSwedish National Infrastructure for Computing (SNIC)Available from: 2016-11-29 Created: 2016-11-29 Last updated: 2018-10-10Bibliographically approved
In thesis
1. Theoretical methods for the electronic structure and magnetism of strongly correlated materials
Open this publication in new window or tab >>Theoretical methods for the electronic structure and magnetism of strongly correlated materials
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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).

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2017. p. 109
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1461
Keywords
dynamical mean field theory (DMFT), Hubbard I approximation, strongly correlated systems, rare earths, lanthanides, photoemission spectra, ultrafast magnetization dynamics, analytic continuation, Padé approximant method, two-particle Green's functions, linear muffin tin orbitals (LMTO), density functional theory (DFT), cerium, stacking fault energy.
National Category
Natural Sciences Physical Sciences
Research subject
Physics with spec. in Atomic, Molecular and Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-308699 (URN)978-91-554-9770-5 (ISBN)
Public defence
2017-02-03, Ång/10132, Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 09:15 (English)
Opponent
Supervisors
Available from: 2017-01-12 Created: 2016-11-29 Last updated: 2017-01-17
2. Theoretical and Computational Studies of Strongly Correlated Electron Systems: Dynamical Mean Field Theory, X-ray Absorption Spectroscopy and Analytical Continuation
Open this publication in new window or tab >>Theoretical and Computational Studies of Strongly Correlated Electron Systems: Dynamical Mean Field Theory, X-ray Absorption Spectroscopy and Analytical Continuation
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis encompasses theoretical and computational studies of strongly correlated elec-tron systems. Understanding how electrons in solids interact with each other is of great im-portance for future technology and other applications. From a fundamental point of view, the Coulomb interaction in a solid leads to a very challenging many-body problem, encapsulating many physical phenomena, e.g. magnetism. Treating this interaction, with a focus on local contributions, is the subject of this thesis. Both models and materials have been investigated, to obtain insight on the mechanisms determining the macroscopic properties of matter. This thesis is divided in four parts, each corresponding to a different project or topic.

In the first project a many body method called dynamical mean field theory (DMFT) is used to study the paramagnetic phase of the Hubbard model. A stochastic version of the exact di-agonalization technique is developed for solving the effective impurity model arising in DMFT and generating real frequency spectral functions. In the next project, by combining density functional theory (DFT) with a static solution of the DMFT equations (DFT+U), magnetic ex-change interactions in transition metal oxides (TMOs) are investigated. The spin dependence of the functional is shown to be important for mapping magnetic excitations form the quantum mechanical system to a classical model.

The next topic in this thesis concerns the x-ray absorption spectroscopy of TMOs. Spectral functions, in good agreement with experimental data, are calculated by combining DFT with multiplet ligand field theory (MLFT). The effects of the presence of a core-hole are studied in detail for NiO, as well as double counting issues related to higher order terms of the multiple ex-pansion of the Coulomb interaction. A strained induced linearly polarized spectrum is obtained for CaTiO3. Lastly, charge disproportionation is seen in Mo doped LaFeO3.

Finally, a critical step in DMFT, called analytical continuation, to obtain physical observ-ables of interest is investigated. Analytical continuation means a transformation of a function in the complex plane. Several methods for performing this transformation are explained, and in particular steps for improving the robustness and accuracy of the Padé approximant method are described.

Place, publisher, year, edition, pages
Uppala: Acta Universitatis Upsaliensis, 2018. p. 112
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1729
National Category
Condensed Matter Physics
Research subject
Physics with spec. in Atomic, Molecular and Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-362834 (URN)978-91-513-0471-7 (ISBN)
Public defence
2018-11-30, Polhemsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Opponent
Supervisors
Note

the opponents university is University of Bremen

Available from: 2018-11-09 Created: 2018-10-10 Last updated: 2018-11-19

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Schött, JohanLocht, Inka L. M.Di Marco, Igor

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