In this paper a duality between the d=2 Wen-plaquette model in a transverse field and the d=1 Ising model in a transverse field is used to learn the nature of the quantum phase transition (QPT) between a spin-polarized phase and a topological ordered state with the string-net condensation. The QPT is not induced by spontaneous symmetry breaking and there are no conventional Landautype local order parameters. Instead the string-like non-local order parameters are introduced to describe the QPT. In particular, the duality character between the open-string and closed string for the QPT are explored.

The crossover from thermal hopping to quantum tunneling is studied. We show that the decay rate-with dissipation can accurately be determined near the crossover temperature. Besides considering the Wentzel-Kramers-Brillouin (WKB) exponent, we also calculate contribution of the fluctuation modes around the saddle point and give an extended account of a previous study of crossover region. We deal with two dangerous fluctuation modes whose contribution can't be calculated by the steepest descent method and show that higher order couplings between the two dangerous modes need to be taken into considerations. At last the crossover from thermal hopping to quantum tunneling in the molecular agnet Mn12Ac is studied.

We propose a model of coupled local moments and itinerant electrons to describe the iron-based superconductors. Here the spin-density-wave (SDW) order of the itinerant electrons is not driven by Fermi surface nesting but is induced by the Hund's rule coupling with the local moments. The superconducting pairing is of the same origin whose strength can reach strong coupling. The existence of the local moments is supported by various anomalous magnetic properties which are in quantitative agreement with experiments.