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

TL;DR

This paper explores how the phase diagram of half-filled multicomponent fermionic cold atoms in one dimension varies with the number of components, revealing a parity-dependent emergence of Haldane insulating phases or metallic behavior.

Contribution

It introduces a Haldane-charge conjecture linking the parity of the number of components to distinct insulating or metallic phases, supported by conformal field theory and DMRG calculations.

Findings

Haldane insulating phases occur for even N with attractive interactions

Metallic behavior with quasi-long range pairing occurs for odd N greater than 1

Haldane phases with N/2 even are topologically trivial, confirming recent conjectures

Abstract

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)].