Energy level statistics of the two-dimensional Hubbard model at low filling

The energy level statistics of the Hubbard model for $L \times L$ square lattices (L=3,4,5,6) at low filling (four electrons) is studied numerically for a wide range of the coupling strength. All known symmetries of the model (space, spin and pseudospin symmetry) have been taken into account explicitly from the beginning of the calculation by projecting into symmetry invariant subspaces. The details of this group theoretical treatment are presented with special attention to the nongeneric case of L=4, where a particular complicated space group appears. For all the lattices studied, a significant amount of levels within each symmetry invariant subspaces remains degenerated, but except for L=4 the ground state is nondegenerate. We explain the remaining degeneracies, which occur only for very specific interaction independent states, and we disregard these states in the statistical spectral analysis. The intricate structure of the Hubbard spectra necessitates a careful unfolding procedure, which is thoroughly discussed. Finally, we present our results for the level spacing distribution, the number variance $\Sigma^2$, and the spectral rigidity $\Delta_3$, which essentially all are close to the corresponding statistics for random matrices of the Gaussian ensemble independent of the lattice size and the coupling strength. Even very small coupling strengths approaching the integrable zero coupling limit lead to the Gaussian ensemble statistics stressing the nonperturbative nature of the Hubbard model.Comment: 31 pages (1 Revtex file and 10 postscript figures

Constraints on neutrino oscillation parameters from the measurement of day-night solar neutrino fluxes at Super-Kamiokande

A search for day-night variations in the solar neutrino flux resulting from neutrino oscillations has been carried out using the 504 day sample of solar neutrino data obtained at Super-Kamiokande. The absence of a significant day-night variation has set an absolute flux independent exclusion region in the two neutrino oscillation parameter space.Comment: 11 pages, 3 figures, submitted to PRL, single-spacin

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