Haldane charge conjecture in one-dimensional multicomponent fermionic cold atoms
Résumé
A Haldane conjecture is revealed for spin-singlet charge modes in 2N-component fermionic cold atoms loaded into one-dimensional optical lattice. By means of a low-energy approach and DMRG calculations, we show the emergence of gapless and gapped phases depending on the parity of N for attractive interactions at half-filling. In particular, the analogue of the Haldane phase of the spin-1 Heisenberg chain is stabilized for N = 2 with non-local string charge correlation, and pseudo-spin 1/2 edge states. At the heart of this even-odd behavior is the existence of spin-singlet pseudo-spin N/2 operator which governs the low-energy properties of the model for attractive interactions and give rise to the Haldane physics.