Motivated by the recent discovery of a spin liquid phase for the Hubbard model on the honeycomb lattice at half-filling, we apply both perturbative and non-perturbative techniques to derive effective spin Hamiltonians describing the low-energy physic
s of the Mott-insulating phase of the system. Exact diagonalizations of the so-derived models on small clusters are performed, in order to assess the quality of the effective low-energy theory in the spin-liquid regime. We show that six-spin interactions on the elementary loop of the honeycomb lattice are the dominant sub-leading effective couplings. A minimal spin model is shown to reproduce most of the energetic properties of the Hubbard model on the honeycomb lattice in its spin-liquid phase. Surprisingly, a more elaborate effective low-energy spin model obtained by a systematic graph expansion rather disagrees beyond a certain point with the numerical results for the Hubbard model at intermediate couplings.
We present a robust scheme to derive effective models non-perturbatively for quantum lattice models when at least one degree of freedom is gapped. A combination of graph theory and the method of continuous unitary transformations (gCUTs) is shown to
efficiently capture all zero-temperature fluctuations in a controlled spatial range. The gCUT can be used either for effective quasi-particle descriptions or for effective low-energy descriptions in case of infinitely degenerate subspaces. We illustrate the method for 1d and 2d lattice models yielding convincing results in the thermodynamic limit. We find that the recently discovered spin liquid in the Hubbard model on the honeycomb lattice lies outside the perturbative strong-coupling regime. Various extensions and perspectives of the gCUT are discussed.
(abbreviated) We present the first results of the ESO large program, ``IMAGES which aims at obtaining robust measurements of the kinematics of distant galaxies using the multi-IFU mode of GIRAFFE on the VLT. 3D spectroscopy is essential to robustly m
easure the often distorted kinematics of distant galaxies (e.g., Flores et al. 2006). We derive the velocity fields and $sigma$-maps of 36 galaxies at 0.4<z<0.75 from the kinematics of the [OII] emission line doublet, and generate a robust technique to identify the nature of the velocity fields based on the pixels of the highest signal-to-noise ratios (S/N). We have gathered a unique sample of 63 velocity fields of emission line galaxies (W0([OII]) > 15 A) at z=0.4-0.75, which are a representative subsample of the population of M_stellar>1.5x10^{10} M_sun emission line galaxies in this redshift range, and are largely unaffected by cosmic variance. Taking into account all galaxies -with or without emission lines- in that redshift range, we find that at least 41+/-7% of them have anomalous kinematics, i.e., they are not dynamically relaxed. This includes 26+/-7% of distant galaxies with complex kinematics, i.e., they are not simply pressure or rotationally supported. Our result implies that galaxy kinematics are among the most rapidly evolving properties, because locally, only a few percent of the galaxies in this mass range have complex kinematics.
