Projects

Orbital-Ordering in Transition-Metal Compounds

Many transition-metal compounds show long-range ordering of the orbital occupation. This effect is somewhat analogous to magnetic ordering like antiferromagnetism, where instead of an ordering of the spins we observe an ordering of the orbitals. As magnetic ordering can be used, e.g., for designing novel devices (spintronics), orbital physics holds the promise of even more versatile device applications (orbitronics). In order to exploit such orbital degrees of freedom, we have, however, first to understand the mechanisms underlying the ordering. Two mechanisms are known that can lead to orbital ordering: electron-phonon coupling leading to a Jahn-Teller distortion, or a purely electronic super-exchange mechanism analogous to that leading to antiferromagnetism. We have developed a method that, for the first time, lets us distinguish these two mechanisms and thus allows us to predict the importance of orbital physics in transition-metal compounds. With this approach we have analyzed the paradigmatic orbitally ordered KCuF3 and the parent compound of the colossal magneto-resistance materials, LaMnO3. Continuing our collaboration with the group of Prof. Pavarini at the IAS/IFF, further systematic studies of orbital-ordering are underway.

Building Realistic Models for Correlated Organics

Organic crystals show a wide variety of unusual effects. Even though they do not contain any metal atoms they can be highly conducting, even superconducting, they have interesting magnetic phases, or show effects of low dimensionality, like spin-charge separation. At the same time the possibility of modifying the molecular building blocks gives vast opportunities for creating designer materials. The unusual physics of the organics is a result of electron correlations: The molecular orbitals overlap only weakly, giving rise to quite narrow bands. There-fore the repulsion between electrons becomes so important that it cannot be described using mean-field approaches. For the description of such strongly correlated materials we have to resort to model Hamiltonians. These generalized Hubbard models have to be simple enough that they can be treated by non-perturbative many-body approaches, yet sufficiently complex to capture the specifics of real materials. We have developed a systematic approach for deriving such realistic model Hamiltonians for molecular crystals ab-initio. In particular, we succeeded in calculating the critical dependence of the hopping matrix elements on the molecular orientations and on the calculation of screened Coulomb matrix elements. Using these realistic models we can understand the unusual effects seen in organic charge-transfer salts like the decay of the electron into a spin and a charge degree of freedom in the quasi one-dimensional metal TTF-TCNQ or the superconductivity in the quasi two-dimensional BEDT-TTF salts. This work is done in collaboration with groups at Frankfurt and Würzburg Uni-versity (theory: Prof. Valentí, experiment: Prof. Claessen). Further developments on modeling the interaction between the organic molecules in the crystal will be done in collaboration with the group of Prof. Carloni.

Multiplets in Solids

A crucial question for the understanding of spin- and orbital degrees of freedom is the interplay between atomic multiplets and kinetic energy in the correlated solid. In the past it was impossible to approach this problem systematically, as the description of multiplets in a solid requires an exponential number of Slater determinants, i.e., is practically impossible. Here dynamical mean-field theory brings us a decisive step forward. Instead of a full lattice, we only have to explicitly describe a single correlated site. This makes the problem tractable, albeit still very difficult to solve. We approach the problem from two complementary directions: using our massively parallel Lanczos solver, we can calculate the multiplet states, however available memory restricts us to finite bath-parametrizations. The second approach uses quantum Monte Carlo to solve the problem for the full bath, where we have, however, to fight with the infamous Fermion sign-problem, which makes the calculations extremely time-consuming, even on a machine like Jugene. This work is done in collaboration with the groups of Prof. Pavarini (IAS/IFF) and Prof. Lichtenstein (Universität Hamburg).

Dynamical Correlation Functions in Dynamical Mean-Field Theory

So far, calculations for strongly correlated materials are mostly restricted to the determination of the spectral function, as this is the quantity that is directly accessible in dynamical mean-field theory. The spectral function contains important information about the excited states of the system, allows us to decide if a system is metallic or insulating and exhibits the dispersion of quasiparticle- or hole-excitations. From the point of technological applications, the main interest in strongly correlated materials is, however, their delicate response to external influences, which makes them ideal candidates for novel electronic, spintronic or orbitronic devices. Still, calculating response functions remains a formidable problem, even in the dynamical mean-field framework. While calculating the susceptibility of an impurity model is straightforward, obtaining the response-function for a solid requires the determination of the dynamical vertices, which then are used to obtain the lattice susceptibility from the solution of a Bethe-Salpeter equation. We have recently been able to compute the first response functions for simple one-band Hubbard and periodic Anderson models, and are now working towards making calculations also for more realistic models possi-ble. This will be a key step on the road to rational materials design. Work on sus-ceptibilities is done in collaboration with the group of Prof. Kotliar (Rutgers University).

Massively Parallel Implementations

Realistic simulations of correlated materials have only become possible with the recent introduction of parallel supercomputers that can sustain the needed com-puting power. Efficiently using a massively parallel machine like the Jülich Blue Gene is, however, far from straightforward. Even running on ten thousand processors, a code that has a mere one percent of serial parts, will only achieve a meager speedup of a factor of one hundred, i.e., the processors will be idle most of the time. In addition parallelization typically introduces a communication overhead. This makes it clear that algorithms that take advantage of the new supercomputer architectures need to be redesigned from ground up. We have already managed to re-implement most of our many-body solvers so that they achieve near ideal speedup on several ten thousands of processors. Only these efficient re-implementations make the simulations described above possible. In close contact with the Jülich Supercomputer Centre we are following the devel-opments in new supercomputer architectures, e.g. the Cell processor, to be able to also efficiently utilize the architectures of the next generations.