Many-body effects in Landau levels: Non-commutative geometry and squeezed correlated states

We discuss symmetry-driven squeezing and coherent states of few-particle systems in magnetic fields. An operator approach using canonical transformations and the SU(1,1) algebras is developed for considering Coulomb correlations in the lowest Landau levels.Comment: 3 pages, 2 figures; to be reported at 17th Int. Conf. on High Magnetic Fields in Semiconductor Physics, Wuerzburg, Germany, July 30 - Aug 4, 200

Electronic correlations and competing orders in multiorbital dimers: a cluster DMFT study

We investigate the violation of the first Hund's rule in 4$d$ and 5$d$ transition metal oxides that form solids of dimers. Bonding states within these dimers reduce the magnetization of such materials. We parametrize the dimer formation with realistic hopping parameters and find not only regimes, where the system behaves as a Fermi liquid or as a Peierls insulator, but also strongly correlated regions due to Hund's coupling and its competition with the dimer formation. The electronic structure is investigated using the cluster dynamical mean-field theory for a dimer in the two-plane Bethe lattice with two orbitals per site and $3/8$-filling, that is three electrons per dimer. It reveals dimer-antiferromagnetic order of a high-spin (double exchange) state and a low-spin (molecular orbital) state. At the crossover region we observe the suppression of long-range magnetic order, fluctuation enhancement and renormalization of electron masses. At certain interaction strengths the system becomes an incoherent antiferromagnetic metal with well defined local moments.Comment: 11 pages, 10 figure

Division subspaces and integrable kernels

In this note we prove that the reproducing kernel of a Hilbert space satisfying the division property has integrable form, is locally of trace class, and the Hilbert space itself is a Hilbert space of holomorphic functions.Comment: 11 page