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The phase diagram of one-dimensional alkaline-earth fermionic atoms and ytterbium 171 atoms is investigated by means of a low-energy approach and density-matrix renormalization group calculations. For incommensurate filling, four gapless phases with a spin gap are found and consist of two superconducting instabilities and two coexisting bond and charge density-waves instabilities. In the half-filled case, seven Mott-insulating phases arise with the emergence of four non-degenerate phases with exotic hidden orderings. [ABSTRACT FROM AUTHOR]

We investigate the possible formation of a molecular condensate, which might be, for instance, the analogue of the alpha condensate of nuclear physics, in the context of multicomponent cold atoms fermionic systems. A simple paradigmatic model of N-component fermions with contact interactions loaded into a one-dimensional optical lattice is studied by means of low-energy and numerical approaches. For attractive interaction, a quasi-long-range molecular superfluid phase, formed from bound-states made of N fermions, emerges at low density. We show that trionic and quartetting phases, respectively for N = 3,4, extend in a large domain of the phase diagram and are robust against small symmetry-breaking perturbations. [ABSTRACT FROM AUTHOR]

We discuss the nature of criticality in the β2=2πN self-dual extension of the sine-Gordon model. This field theory is related to the two-dimensional classical XY model with a N-fold degenerate symmetry-breaking field. We briefly overview the already studied cases N=2,4 and analyze in detail the case N=3 where a single phase transition in the three-state Potts universality class is expected to occur. The Z3 infrared critical properties of the β2=6π self-dual sine-Gordon model are derived using two non-perturbative approaches. On one hand, we map the model onto an integrable deformation of the Z4 parafermion theory. The latter is known to flow to a massless Z3 infrared fixed point. Another route is based on the connection with a chirally asymmetric, su(2)4⊗su(2)1 Wess–Zumino–Novikov–Witten model with anisotropic current–current interaction, where we explore the existence of a decoupling (Toulouse) point. [Copyright &y& Elsevier]

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]