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Accueil du site > Publications > Publications 2011 > Competing orders in one-dimensional half-filled multicomponent fermionic cold atoms : The Haldane-charge conjecture

## Competing orders in one-dimensional half-filled multicomponent fermionic cold atoms : The Haldane-charge conjecture

H. Nonne, P. Lecheminant, S. Capponi, G. Roux, and E. Boulat

par - 18 juillet 2011

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 \emphnot 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)].