Research topics

The many-particle theory group investigates correlated electron systems.

We currently investigate the following topics.

  • Optical excitations in polymers

    Pi-conjugated polymers are quasi one-dimensional insulators. They are characterized by a bond alternation as is seen in the simplest polymer, trans-polyacetylene, (CH)n , where long and short bonds alternate (Peierls distortion). Up to an excitation energy of three electron volts, the opto-electronic properties of polymers are dominated by the pi-electron system which consists of molecular orbitals formed by the pz orbitals on each carbon atom so that the pi-electron system is frequently approximated by a half-filled Hückel chain.

    The Coulomb interaction between the pi-electrons is substantial. The local (Hubbard) interaction on each carbon atom increases the bond alternation and the size of the single-particle gap that is about 2 eV.  The long-range part of the Coulomb interaction is important for the large exciton binding energy of about 0.5 eV. Only a correlated-electron theory explains the experimental values consistently whereas theories based on a strong electron-phonon interaction cannot explain the data consistently.

    The parameters for a realistic Hückel-Hubbard-Ohno model are deduced from quantum-chemical calculations and from a comparison with experiment. Reasonable values are W=10...11 eV for the pi-electron bandwidth, a=4 eV/A for the Peierls coupling, U=6 eV for the Hubbard interaction, and V=3 eV for the Ohno parameter. The spring constant for the sigma bonds is about K= 42 eV/A2.

    Currently, we are investigating the optical phonon spectrum of trans-polyacetylene in more detail. For a Hubbard chain without the hydrogen atoms, the carbon optical phonon modes are in the correct regime of about 1000 cm-1.

    Related publications:

    Optical phonons for Peierls chains with long-range Coulomb interactions
    Máté Timar, Gergely Barcza, Florian Gebhard, and Örs Legeza, Phys. Rev. B 95, 085150 (2017).

    Hückel-Hubbard-Ohno modeling of pi-bonds in ethene and ethyne with application to trans-polyacetylene
    Máté Timar, Gergely Barcza, Florian Gebhard, Libor Veis, and Örs Legeza, Phys. Chem. Chem. Phys. 18, 18835 (2016).

    Excited states in polydiacetylene chains: A density matrix renormalization group study
    Gergely Barcza, William Barford, Florian Gebhard, and Örs Legeza, Phys. Rev. B 87, 245116 (2013).

    Density matrix renormalization group study of excitons in polydiacetylene chains
    Gergely Barcza,  Örs Legeza, Florian Gebhard, and Reinhard Noack, Phys. Rev. B 81, 045103 (2010).

    Perturbation theory for optical excitations in the one-dimensional extended Peierls-Hubbard model
    Anja Grage, Florian Gebhard, and Jörg Rissler, J. Stat. Mech. Exp. Theor. P08009 (2005).

    Excited states of ladder-type poly-p-phenylene oligomers
    Jörg Rissler, Heinz Bässler, Florian Gebhard, and Peter Schwerdtfeger, Phys. Rev. B 64, 045122 (2001).

    Excitons in one-dimensional Mott insulators
    Fabian H.L. Essler, Florian Gebhard, and Eric Jeckelmann, Phys. Rev. B 64, 125119 (2001).

    Optical conductivity of the half-filled Hubbard chain
    Eric Jeckelmann, Florian Gebhard, and Fabian H.L. Essler, Phys. Rev. Lett. 85, 3910 (2000).

  • Itinerant magnetism

    The theoretical description of metallic magnetism poses a difficult many-particle problem. In textbooks, only the simple Stoner picture of band ferromagnetism is presented. Fermi statistics for the electrons dictates that electrons with like spins are unlikely to be close to each other (Pauli or exchange hole in the density-density correlation function). Therefore, the Coulomb repulsion is less efficient for electrons with the same spin orientation than for electrons with different spin orientation. This energy gain due to statistics is known as the exchange energy. If the gain in exchange energy overcomes the loss in kinetic energy, the metal becomes ferromagnetic (Stoner criterion). This argument is known to apply very well in atoms (first Hund's rule) as it gives rise to local magnetic moments in atoms with partially filled shells.

    The simple Stoner picture explains why iron, cobalt, and nickel are ferromagnets but it fails to describe the presence of local moments also in transition metals. Moreover, in Stoner theory and its modern variant, spin-density function theory, SDFT, the metallic binding provided by the narrow d-electron bands is too strong so that the d-electron bandwidths are too large and the lattice constants are too small.

    These problems are cured when electron-electron correlations are taken into account within the fairly simple-minded Gutzwiller variational approach. The evaluation of Gutzwiller-type wave states poses a true many-particle problem. Fortunately, it can be worked out in the limit of large coordination number (Z=12 in fcc nickel) without further approximations. However, the remaining optimization of the quasi-particle bandstructure still requires sophisticated minimization algorithms. The Gutzwiller approach can be combined with density function theory (DFT) to the Gutzwiller-DFT for the calculation of quasi-particle bands for correlated transition metals and their compounds. Results for nickel and iron show a fairly good agreement with experiment when U=10 eV and J=0.6 eV are used for the underlying multi-band Hubbard models.

    More recently, we studied magnetic impurities in semiconductors and in metals. The coupling of magnetic impurities in an insulating matrix can be well understood from indirect exchange interactions. The parameters can be deduced from energy considerations based on band-structure theory. The coupling of impurities in metals is more subtle, and is currently under investigation in our group.

    Related publications:

    Gutzwiller variational approach to the two-impurity Anderson model for a metallic host at particle-hole symmetry
    Thorben Linneweber, Jörg Bünemann, Zakaria M.M. Mahmoud, and Florian Gebhard, J. Phys.: Condens. Matter 29, 445603 (2017).

    Non-interacting two-impurity Anderson model on a lattice at particle-hole symmetry
    Zakaria M.M. Mahmoud, Jörg Bünemann, and Florian Gebhard, phys. stat. sol (b), 1600842 (2017).

    Coulomb matrix elements in multi-orbital Hubbard models
    Jörg Bünemann and Florian Gebhard, J. Phys. Cond. Matt. 29, 165601 (2017).

    Exchange couplings for Mn ions in CdTe: Validity of spin models for dilute magnetic II-VI semiconductors
    Thorben Linneweber, Jörg Bünemann, Ute Löw, Florian Gebhard, and Frithjof Anders, Phys. Rev. B 95, 045134 (2017).

    Approximation schemes for the study of multi-band Gutzwiller wave functions
    Jörg Bünemann, Thorben Linneweber, and Florian Gebhard, phys. stat. sol. (b) 254, 1600166 (2017).

    Interplay of Coulomb interaction and spin-orbit coupling
    Jörg Bünemann, Thorben Linneweber, Ute Löw, Frithjof B. Anders, and Florian Gebhard, Phys. Rev. B 94, 035116 (2016).

    Quasiparticle bands and structural phase transition of iron from Gutzwiller density-functional theory
    Tobias Schickling, Jörg Bünemann, Florian Gebhard, and Lilia Boeri, Phys. Rev. B 93, 205151 (2016).

    Gutzwiller density functional theory: a formal derivation and application to nickel
    Tobias Schickling, Jörg Bünemann, Florian Gebhard, and Werner Weber, New J. Phys. 16, 093034 (2014).

    Numerical minimisation of Gutzwiller energy functionals
    Jörg Bünemann, Florian Gebhard, Tobias Schickling, and Werner Weber, phys. stat. sol. (b) 249, 1282 (2012).

    Gutzwiller Theory of Band Magnetism in LaOFeAs
    Tobias Schickling, Florian Gebhard, Jörg Bünemann, Lilia Boeri, Ole K. Andersen, and Werner Weber, Phys. Rev. Lett. 108, 036406 (2012).

    Antiferromagnetic order in multiband Hubbard models for iron pnictides
    Tobias Schickling, Florian Gebhard, and Jörg Bünemann, Phys. Rev. Lett. 106, 146402 (2011).

    Renormalization of bulk magnetic electron states at high binding energies
    Andreas Hofmann, Xiaoyu Cui, Jörg Schäfer, Sebastian Meyer, Philipp Höpfner, Christian Blumenstein, Markus Paul, Luc Patthey, Eli Rotenberg, Jörg Bünemann, Florian Gebhard, Torsten Ohm, Werner Weber, and Ralph Claessen, Phys. Rev. Lett. 102, 187204 (2009).

    Spin-orbit coupling in ferromagnetic nickel
    Jörg Bünemann, Florian Gebhard, Torsten Ohm, Stefan Weiser, and Werner Weber, Phys. Rev. Lett. 101, 236404 (2008).

    Equivalence of Gutzwiller and slave-boson mean-field theories for multiband Hubbard models
    Jörg Bünemann and Florian Gebhard, Phys. Rev. B 76, 193104 (2007).

    Atomic correlations in itinerant ferromagnets: Quasi-particle bands of nickel
    J. Bünemann, F. Gebhard, T. Ohm, R. Umstätter, S. Weiser, W. Weber, R. Claessen, D. Ehm, A. Harasawa, A. Kakizaki, A. Kimura, G. Nicolay, S. Shin, and V.N. Strocov, Europhys. Lett. 61, 667 (2003).

    Multi-band Gutzwiller wave functions for itinerant ferromagnetism
    Jörg Bünemann, Florian Gebhard, and Werner Weber, Found. of Physics 30, 2011 (2000).

    Multi-band Gutzwiller wave functions for general on-site interactions
    Jörg Bünemann, Werner Weber, and Florian Gebhard, Phys. Rev. B 57, 6896 (1998).