Aperiodic order and quasicrystals: spectral properties

We present spectral theoretic results for Hamiltonians associated with Delone sets. For a family of discrete models we characterize the appearance of jumps in the integrated density of states. For a family of continuum models on the set of all Delone sets with suitable parameters we prove that generically purely singular continuous spectrum occurs

Resonating-valence-bond theory for the square-planar lattice

The short-range resonating-valence-bond (RVB) wave function with nearest-neighbor (NN) spin pairings only is investigated as a possible description for the Heisenberg model on a square-planar lattice. A type of long-range order associated to this RVB Ansatz is identified along with some qualitative consequences involving lattice distortions, excitations, and their coupling