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

Understand

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.