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Dynamical Mean Field Theory-Based Electronic Structure Calculations for Correlated Materials

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First Principles Approaches to Spectroscopic Properties of Complex Materials

Part of the book series: Topics in Current Chemistry ((TOPCURRCHEM,volume 347))

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Abstract

We give an introduction to dynamical mean field approaches to correlated materials. Starting from the concept of electronic correlation, we explain why a theoretical description of correlations in spectroscopic properties needs to go beyond the single-particle picture of band theory.

We discuss the main ideas of dynamical mean field theory and its use within realistic electronic structure calculations, illustrated by examples of transition metals, transition metal oxides, and rare-earth compounds. Finally, we summarise recent progress on the calculation of effective Hubbard interactions and the description of dynamical screening effects in solids.

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Notes

  1. 1.

    For a review of the Mott transition comprising a discussion of coherence–decoherence crossovers see, e.g. [5].

  2. 2.

    A many-body Hamiltonian is called separable if it can be written as a sum over operators each acting only on one electron.

  3. 3.

    Even though it is of course always possible to design an auxiliary one-particle system for the purpose of parametrising certain physical quantities, such as the density, as done in the Kohn-Sham construction of density functional theory.

  4. 4.

    We do not enter here into the subtle questions of frustrations leading to possible spin liquid phases.

  5. 5.

    Due to the presence of only two electrons, with different spins, the simple one-orbital model did not involve any effects of electronic exchange.

  6. 6.

    This also means that we are not entering into an exhaustive discussion of what should be the “best” starting one-body picture to build DMFT on. The section on GW + DMFT contains some implicit information on this issue, but systematic comparisons have not been performed so far (see however the discussion in [16]).

  7. 7.

    And not even a Slater determinant.

  8. 8.

    This part can in fact be thought of as comprising, apart from the kinetic energy, any one-body potential, e.g. the electrostatic potential created by the ions.

  9. 9.

    The interaction v screened(r,r′) is not simply the bare Coulomb interaction 1/(|r − r′ |) but rather a partially screened version of it. This issue will be the subject of Sect. 12, which describes recent developments in the field.

  10. 10.

    DMFT has been the subject of several extended review articles, see, e.g. [24–26].

  11. 11.

    Calculating photoemission intensities strictly speaking involves further modelling steps, including in particular matrix elements describing the coupling of the light field to the electrons of the solid. We do not enter into this discussion here, but restrict ourselves to discussing the spectral function.

  12. 12.

    We note that, crystallographically, a tetragonally distorted fcc phase, is described as a bct lattice.

  13. 13.

    The same is true for quasi-one-dimensional systems, where one-dimensional chains provide natural entities to be treated as clusters; see the applications of “chain-DMFT” in [111–114].

  14. 14.

    Thus non-local in the electronic structure sense.

  15. 15.

    Even though the latter is not derived from a local potential.

  16. 16.

    With n R = ΣL,σ n RLσ the number operator of electrons in localised orbitals L on atom R with spin σ.

  17. 17.

    The situation is somewhat more subtle when more exotic kinds of ordering are involved, such as orbital- or charge order. Still, the general remark about the resulting spectrum being strictly a band structure holds.

  18. 18.

    In fact, the ability to determine the full frequency-dependence is probably the most important conceptual advance over traditional strategies aiming at the calculation of the static interactions only. In this category, we mention “constrained LDA” techniques, pioneered in [129, 130] as well as linear response schemes [131–133] and GW-inspired techniques [134].

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Acknowledgements

My view on the field, and specifically on the work summarised here, has been influenced over the years by discussions and collaborations with numerous colleagues. I thank in particular M. Aichhorn, F. Aryasetiawan, M. Casula, M. Ferrero, A. Georges, M. Katsnelson, F. Lechermann, A.I. Lichtenstein, C. Martins, O. Parcollet, L. Pourovskii, A. Rubtsov, J.M. Tomczak, L. Vaugier and V. Vildosola most warmly for the fruitful and enjoyable collaborations. I also thank P. Seth for her careful reading of the manuscript.

This work was supported by the French ANR under projects SURMOTT and PNICTIDES, and IDRIS/GENCI under project 139313.

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  1. Centre de Physique Théorique, Ecole Polytechnique, CNRS UMR7644, Palaiseau, 91128, France

    Silke Biermann

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  1. Silke Biermann
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  1. Dipartimento di Scienza dei Materiali, Università di Milano-Bicocca, via Cozzi 55 20125, Milano, Italy

    Cristiana Di Valentin

  2. UMR5306 Université Lyon 1-CNRS Université Lyon, Institut Lumière Matière and ETSF, Villeurbanne, France

    Silvana Botti

  3. Éole polytechnique fédérale de Lausanne, Institute of Materials, Lausanne, Switzerland

    Matteo Cococcioni

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Biermann, S. (2014). Dynamical Mean Field Theory-Based Electronic Structure Calculations for Correlated Materials. In: Di Valentin, C., Botti, S., Cococcioni, M. (eds) First Principles Approaches to Spectroscopic Properties of Complex Materials. Topics in Current Chemistry, vol 347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/128_2014_530

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