One-dimensional two-orbital SU(N) ultracold fermionic quantum gases at incommensurate filling: a low-energy approach

We investigate the zero-temperature phase diagram of two-orbital SU(N) fermionic models at incommensurate filling which are directly relevant to strontium and ytterbium ultracold atoms loading into a one-dimensional optical lattice. Using a low-energy approach that takes into account explicitly the SU(N) symmetry, we find that a spectral gap for the nuclear-spin degrees of freedom is formed for generic interactions. Several phases with one or two gapless modes are then stabilized which describe the competition between different density instabilities. In stark contrast to the N=2 case, no dominant pairing instabilities emerge and the leading superfluid one is rather formed from bound states of 2N fermions.Comment: 11 pages, 4 figure

Lattice spin models for non-Abelian Chiral Spin Liquids

We suggest a class of two-dimensional lattice spin Hamiltonians describing non-Abelian SU(2) chiral spin liquids - spin-analogues of fractional non-Abelian quantum Hall states- with gapped bulk and gapless chiral edge excitations described by the SU(2)$_n$ Wess-Zumino-Novikov-Witten conformal field theory. The models are constructed from an array of a generalized spin-$n/2$ ladders with multi-spin exchange interaction which are coupled by isolated spins. Such models allow a controllable analytic treatment starting from the one-dimensional limit and are characterized by a bulk gap and non-Abelian SU(2)$_n$ gapless edge excitations.Comment: 7 pages, one figure, replaced by an updated versio

Quantum phase transitions in multileg spin ladders with ring exchange

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 \le 4