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We present a field-theory analysis of a model of two SU(2n)-invariant magnetic chains coupled by a generic interaction preserving time-reversal and inversion symmetry. Contrary to the SU(2)-invariant case the zero-temperature phase diagram of such two-leg spin ladder does not contain topological phases. Only generalized valence bond solid phases are stabilized when n>1 with different wave vectors and ground-state degeneracies. In particular, we find a phase which is made of a cluster of 2n spins put in an SU(2n) singlet state. For n=3, this cluster phase is relevant to 173Yb ultracold atoms, with an emergent SU(6) symmetry, loaded in a double-well optical lattice. [ABSTRACT FROM AUTHOR]

Four-spin exchange interaction has been raising intriguing questions regarding the exotic phase transitions it induces in two-dimensional quantum spin systems. In this context, we investigate the effects of a cyclic four-spin exchange in the quasi-1D limit by considering a general N-leg spin ladder. We show by means of a low-energy approach that depending on its sign, this ring exchange interaction can engender either a staggered or a uniform dimerization from the conventional phases of spin ladders. The resulting quantum phase transition is found to be described by the SU(2)N conformal field theory. This result, as well as the fractional value of the central charge at the transition, is further confirmed by a large-scale numerical study performed by means of exact diagonalization and density matrix renormalization group approaches for N≤4. [ABSTRACT FROM AUTHOR]

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]

The zero-temperature phase diagram of a p-orbital two-component fermionic system loaded into a one-dimensional optical lattice is mapped out by means of analytical and numerical techniques. It is shown that the p-band model away from half-filling hosts various competing superconducting phases for attractive and repulsive interactions. At quarter-filling, we analyze the possible formation of incompressible Mott phases and in particular for repulsive interactions, we find the occurrence of a Mott transition with the formation of fully gapped bond-ordering waves. [ABSTRACT FROM AUTHOR]

The zero-temperature phase diagram of a p-orbital two-component fermionic system loaded into a one-dimensional optical lattice is mapped out by means of analytical and numerical techniques. It is shown that the p-band model away from half-filling hosts various competing superconducting phases for attractive and repulsive interactions. At quarter-filling, we analyze the possible formation of incompressible Mott phases and in particular for repulsive interactions, we find the occurrence of a Mott transition with the formation of fully gapped bond-ordering waves. [ABSTRACT FROM AUTHOR]

We investigate possible realizations of exotic SU(N) symmetry-protected topological (SPT) phases with alkaline-earth cold fermionic atoms loaded into one-dimensional optical lattices. A thorough study of two-orbital generalizations of the standard SU(N) Fermi-Hubbard model, directly relevant to recent experiments, is performed. Using state-of-the-art analytical and numerical techniques, we map out the zero-temperature phase diagrams at half-filling and identify several Mott-insulating phases. While some of them are rather conventional (nondegenerate, charge-density wave, or spin-Peierls-like), we also identify, for even N, two distinct types of SPT phases: an orbital Haldane phase, analogous to a spin-N/2 Haldane phase, and a topological SU(N) phase, which we fully characterize by its entanglement properties. We also propose sets of nonlocal order parameters that characterize the SU(N) topological phases found here. [ABSTRACT FROM AUTHOR]

The zero-temperature properties of the SO(5) bilinear-biquadratic Heisenberg chain are investigated by means of a low-energy approach and large-scale numerical calculations. In sharp contrast to the spin-1 SO(3) Heisenberg chain, we show that the SO(5) Heisenberg chain is dimerized with a twofold degenerate ground state. On top of this gapful phase, we find the emergence of a nondegenerate gapped phase with hidden (Z2 × Z2)2 symmetry and spin-3/2 edge states that can be understood from a SO(5) AKLT wave function. We derive a low-energy theory describing the quantum critical point which separates these two gapped phases. It is shown and confirmed numerically that this quantum critical point belongs to the SO(5)t universality class. [ABSTRACT FROM AUTHOR]