Abelian flux induced magnetic frustrations of spinor boson superfluids on a square lattice

Inspired by recent experimental advances to generate Abelian flux for neutral cold atoms and photons moving in a lattice, we investigate the possible effects of the $\pi$ flux through a unit cell in the pseudo-spin 1/2 spinor boson Hubbard model in a square lattice. We find that the $\pi$ flux induces a dramatic interplay between the charge and the spin which leads to a frustrated superfluid. We develop a new and systematic "order from quantum disorder" analysis to determine not only the true quantum ground state, but also the excitation spectrum. The superfluid ground state has a 4 sublattice $90^{\circ}$ coplanar spin structure which supports 4 linear gapless modes with 3 different velocities. We speculate the transition from the weak coupling frustrated SF to the strong coupling Ferromagnetic Mott state to be in a new universality class of non-Ginsburg Landau type. These novel phenomena may be observed in these recent cold atom and photonic experiments.Comment: 5 pages, REVTEX-4, 3 figure

Explosive Percolation Obeys Standard Finite-Size Scaling in an Event-based Ensemble

Explosive percolation in the Achlioptas process, which has attracted much research attention, is known to exhibit a rich variety of critical phenomena that are anomalous from the perspective of continuous phase transitions. Hereby, we show that, in an event-based ensemble, the critical behaviors in explosive percolation are rather clean and obey the standard finite-size scaling theory, except for the large fluctuation of pseudo-critical points. In the fluctuation window, multiple fractal structures emerge and the values can be derived from a crossover scaling theory. Further, their mixing effects account well for the previously observed anomalous phenomena. Making use of the clean scaling in the event-based ensemble, we determine with a high precision the critical points and exponents for a number of bond-insertion rules, and clarify ambiguities about their universalities. Our findings hold true for any spatial dimensions.Comment: 5 pages, 4 figure

Variational Bihamiltonian Cohomologies and Integrable Hierarchies III: Linear Reciprocal Transformations

For an integrable hierarchy which possesses a bihamiltonian structure with semisimple hydrodynamic limit, we prove that the linear reciprocal transformation with respect to any of its symmetry transforms it to another bihamiltonian integrable hierarchy. Moreover, we show that the central invariants of the bihamiltonian structure are preserved under such a linear reciprocal transformation