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We investigate the nature of the Mott-insulating phases of half-filled 2N-component fermionic cold atoms loaded into a one-dimensional optical lattice. By means of conformal field theory techniques and large-scale DMRG calculations, we show that the phase diagram strongly depends on the parity of $N$. First, we single out charged, spin-singlet, degrees of freedom, that carry a pseudo-spin ${cal S}=N/2$ allowing to formulate a Haldane conjecture: for attractive interactions, we establish the emergence of Haldane insulating phases when $N$ is even, whereas a metallic behavior is found when $N$ is odd. We point out that the $N=1,2$ cases do emph{not} have the generic properties of each family. The metallic phase for $N$ odd and larger than 1 has a quasi-long range singlet pairing ordering with an interesting edge-state structure. Moreover, the properties of the Haldane insulating phases with even $N$ further depend on the parity of N/2. In this respect, within the low-energy approach, we argue that the Haldane phases with N/2 even are not topologically protected but equivalent to a topologically trivial insulating phase and thus confirm the recent conjecture put forward by Pollmann {it et al.} [Pollmann {it et al.}, arXiv:0909.4059 (2009)].
A Haldane conjecture is revealed for spin-singlet charge modes in 2N-component fermionic cold atoms loaded into a one-dimensional optical lattice. By means of a low-energy approach and DMRG calculations, we show the emergence of gapless and gapped ph
The physical properties of arbitrary half-integer spins F = N - 1/2 fermionic cold atoms loaded into a one-dimensional optical lattice are investigated by means of a conformal field theory approach. We show that for attractive interactions two differ
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, a superconducting state with non-zero total momentum Cooper pairs in a large magnetic field, was first predicted about 50 years ago, and since then became an important concept in many branches of phy
We study a simple model of N-component fermions with contact interactions which describes fermionic atoms with N=2F+1 hyperfine states loaded into a one-dimensional optical lattice. We show by means of analytical and numerical approaches that, for at
A simple set of algebraic equations is derived for the exact low-temperature thermodynamics of one-dimensional multi-component strongly attractive fermionic atoms with enlarged SU(N) spin symmetry and Zeeman splitting. Universal multi-component Tomon