[en] Our general interest is in the properties of ensembles of random Hamiltonians that satisfy a self-consistency property. Such ensembles typically appear in mean-field treatments of interacting systems. The example we here consider is the Superconductor Insulator Transition (SIT) where the superconducting gap is calculated self-consistently in the presence of short-range disorder. Our focus is on disordered films with conventional s-wave pairing that we study numerically employing the negative-U Hubbard model within the standard Bogoliubov-deGennes approximation. The general question that we would like to address here concerns the auto-correlation function of the pairing amplitude: How does it decay in real space and in what way does it change across the SIT? This poster presents our first (preliminary) results. We speculate that our research might have significant impact on the understanding of the SIT if it turns out that the pairing amplitude decays in a power-law fashion (with exponent below two) at the critical point.

[en] Our general interest is in aspects of self-consistency with respect to disorder in the mean-field treatment of disordered interacting systems. The example we here consider is the Superconductor Insulator Transition (SIT), where the superconducting gap is calculated in the presence of short-range disorder. Our focus is on disordered films with conventional s-wave pairing that we study numerically employing the negative-U Hubbard model within the standard Bogoliubov-deGennes approximation. The general question that we would like to address concerns the auto-correlation function of the pairing amplitude: Does it qualitatively change if full self-consistency is accounted for? Our research might have significant impact on the understanding of the SIT, if extra correlations appear due to the self-consistency condition that turn out sufficiently long-ranged. Such correlation effects are ignored in major analytical theories. To study the long-range behavior of the order parameter correlations, the treatment of large system sizes is necessary. Due to the self-consistency requirement, the relevant sizes (e.g. 10${}^6$ sites) are numerically very expensive to achieve. For this reason, we have developed a parallelized code based on the Kernel Polynomial Method. We present data that indicates the existence of very long ranged (power-law) correlations that may indeed change the critical behavior in a significant way.

[en] Our general interest is in the properties of ensembles of random Hamiltonians that satisfy a self-consistency property. Such ensembles typically appear in mean-field treatments of interacting systems. The example we here consider is the Superconductor-Insulator Transition (SIT) where the superconducting gap is calculated self-consistently in the presence of short-range disorder. Our focus is on disordered films with conventional s-wave pairing that we study numerically employing the negative-U Hubbard model within the standard Bogoliubov-deGennes approximation. The general question that we would like to address here concerns the auto-correlation function of the pairing amplitude: How does it decay in real space and in what way does it change across the SIT? These correlations are typically neglected in analytical theories. Our research might have significant impact on the understanding of the SIT, if the correlations turn out sufficiently long-ranged, so that they influence properties of the critical point. We present preliminary data that indicates the existence of very long ranged (power-law) correlations that may indeed change the critical behavior in a significant way.

[en] We study quantum phases and localization-delocalization transitions between these phases in three types of quantum Hall effects. These include the conventional integer quantum Hall effect, as well as its counterparts taking place in superconducting systems: spin quantum Hall effect and thermal quantum Hall effect. A particular emphasis is put on multifractal behavior of wave functions at criticality. (copyright 2008 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

[en] The Sachdev–Ye–Kitaev (SYK) model is a rare example of a strongly-interacting system that is analytically tractable. Tractability arises because the model is largely structureless by design and therefore artificial: while the interaction is restricted to two-body terms, interaction matrix elements are “randomized” and therefore the corresponding interaction operator does not commute with the local density. Unlike conventional density–density-type interactions, the SYK-interaction is, in this sense, not integrable. We here investigate a variant of the (complex) SYK model, which restores this integrability. It features a randomized single-body term and a density–density-type interaction. We present numerical investigations suggesting that the model exhibits two integrable phases separated by several intermediate phases including a chaotic one. The chaotic phase carries several characteristic SYK-signatures including in the spectral statistics and the frequency scaling of the Green’s function and therefore should be adiabatically connected to the non-Fermi liquid phase of the original SYK model. Thus, our model Hamiltonian provides a bridge from the SYK-model towards microscopic realism.

[en] Motivated by recent experiments on electrochemically controlled Pb atomic-scale switches we have studied the self-diffusion of Pb on flat and stepped surfaces since diffusion processes play an important role in the growth of metal substrates. Kinetic modelling based on Monte-Carlo simulations using a model potential suggests that exchange processes play an important role in the contact formation at the nanoscale. Periodic density functional theory indeed find that the barriers for exchange diffusion across the steps are significantly lower than for hopping diffusion. The consequences for the contact formation in electrochemically controlled switches are discussed