Haldane charge conjecture in one-dimensional multicomponent fermionic cold atoms

TL;DR

This paper reveals a Haldane-like conjecture for charge modes in one-dimensional multicomponent fermionic cold atoms, showing parity-dependent phases with gapless or gapped behavior, and identifying a Haldane phase for N=2.

Contribution

It introduces a Haldane charge conjecture in 1D multicomponent fermionic cold atoms, demonstrating parity-dependent phases and identifying a Haldane phase for N=2 with characteristic correlations and edge states.

Findings

Parity of N determines gapless or gapped phases.

N=2 exhibits a Haldane phase with string charge correlations.

Pseudo-spin operators govern low-energy properties for attractive interactions.

Abstract

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 phases depending on the parity of $N$ for attractive interactions at half-filling. 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 a spin-singlet pseudo-spin $N/2$ operator which governs the low-energy properties of the model for attractive interactions and gives rise to the Haldane physics.