Birationally isotrivial fiber spaces

We prove that a family of varieties is birationally isotrivial if all the fibers are birational to each other.Comment: 10 pages; v2: thanks to helpful suggestions of the referee, the main result is now independent of the Eisenbud-Goto conjecture; also we removed the erroneous Prop. 3.4 of v1 which was not needed for anything else in the pape

Extended crossover from Fermi liquid to quasi-antiferromagnet in the half-filled 2D Hubbard model

The ground state of the Hubbard model with nearest-neighbor hopping on the square lattice at half filling is known to be that of an antiferromagnetic (AFM) band insulator for any on-site repulsion. At finite temperature, the absence of long-range order makes the question of how the interaction-driven insulator is realized nontrivial. We address this problem with controlled accuracy in the thermodynamic limit using self-energy diagrammatic determinant Monte Carlo and dynamical cluster approximation methods and show that development of long-range AFM correlations drives an extended crossover from Fermi liquid to insulating behavior in the parameter regime that precludes a metal-to-insulator transition. The intermediate crossover state is best described as a non-Fermi liquid with a partially gapped Fermi surface.Comment: 6 pages, 4 figures, with supplemental material: 2 pages, 3 figure

Neutrinoless double beta decay and neutrino mass hierarchies

In the framework of the see-saw mechanism the normal hierarchy is favorable for the neutrino mass spectrum. For this spectrum we present a detailed calculation of the half-lives of neutrinoless double beta decay for several nuclei of experimental interest. The half-lives are evaluated by considering the most comprehensive nuclear matrix elements, which were obtained within the renormalized QRPA by the Bratislava-Caltech-Tuebingen group. The dependence of the half-lives on sin^2 theta_{13}$ and the lightest neutrino mass is studied. We present also the results of the calculations of the half-lives of neutrinoless double beta decay in the case of the inverted hierarchy of neutrino masses.Comment: 13 pages, 3 figure