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Analytic continuation by averaging Pade approximants
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
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.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory. Harvard Univ, Sch Engn & Appl Sci, Cambridge, MA 02138 USA..
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2016 (English)In: PHYSICAL REVIEW B, ISSN 2469-9950, Vol. 93, no 7, 075104Article in journal (Refereed) Published
Resource type
Text
Abstract [en]

The ill-posed analytic continuation problem for Green's functions and self-energies is investigated by revisiting the Pade approximants technique. We propose to remedy the well-known problems of the Pade approximants by performing an average of several continuations, obtained by varying the number of fitted input points and Pade coefficients independently. The suggested approach is then applied to several test cases, including Sm and Pr atomic self-energies, the Green's functions of the Hubbard model for a Bethe lattice and of the Haldane model for a nanoribbon, as well as two special test functions. The sensitivity to numerical noise and the dependence on the precision of the numerical libraries are analyzed in detail. The present approach is compared to a number of other techniques, i.e., the nonnegative least-squares method, the nonnegative Tikhonov method, and the maximum entropy method, and is shown to perform well for the chosen test cases. This conclusion holds even when the noise on the input data is increased to reach values typical for quantum Monte Carlo simulations. The ability of the algorithm to resolve fine structures is finally illustrated for two relevant test functions.

Place, publisher, year, edition, pages
2016. Vol. 93, no 7, 075104
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:uu:diva-279570DOI: 10.1103/PhysRevB.93.075104ISI: 000369399500001OAI: oai:DiVA.org:uu-279570DiVA: diva2:908412
Funder
Swedish Research CouncileSSENCE - An eScience CollaborationKnut and Alice Wallenberg Foundation, KAW-2013.0020
Available from: 2016-03-02 Created: 2016-03-02 Last updated: 2016-11-29
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. 109 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1461
Keyword
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)
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Supervisors
Available from: 2017-01-12 Created: 2016-11-29 Last updated: 2017-01-17

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Schött, JohanLocht, Inka L. M.Grånäs, OscarEriksson, OlleDi Marco, Igor

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