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We investigate the competition between different orders in the two-leg spin ladder with a ring-exchange interaction by means of a bosonic approach. The latter is defined in terms of spin-1 hard-core bosons which treat the Néel and vector-chirality order parameters on an equal footing. A semiclassical approach of the resulting model describes the phases of the two-leg spin ladder with a ring exchange. In particular, we derive the low-energy effective actions which govern the physical properties of the rung-singlet and dominant vector-chirality phases. As a by-product of our approach, we reveal the mutual induction phenomenon between spin and chirality with, for instance, the emergence of a vector-chirality phase from the application of a magnetic field in bilayer systems coupled by four-spin exchange interactions. [ABSTRACT FROM AUTHOR]

The competition between intertube hopping processes and density-density interactions is investigated in one-dimensional quantum dipolar bosons systems of A' coupled tubes at zero temperature. Using a phenomenological bosonization approach, we show that the resulting competition leads to an exotic quantum phase transition described by a U(l) x Z/v conformai field theory with a fractional central charge. The emerging Zi parafermionic critical degrees of freedom are highly nontrivial in terms of the original atoms or polar molecules of the model. We further determine the main physical properties of the quantum-critical point in a double-tube system which has central charge c = 3/2. In triple-tube systems, we show that the competition between the two antagonistic processes is related to the physics of the two-dimensional Z3 chiral Potts model. This work opens the possibility to study the exotic properties of the Z parafermions in the context of ultracold quantum Bose gases. [ABSTRACT FROM AUTHOR]