"Haldane" phases with ultracold fermionic atoms in double-well optical lattices

TL;DR

This paper proposes realizing SU(N) symmetry-protected topological phases, including Haldane and chiral Haldane phases, using ultracold fermionic atoms in optical lattices, with theoretical models and experimental feasibility discussed.

Contribution

It introduces a realistic model for SU(N) topological phases in cold atoms and identifies new chiral Haldane phases that break inversion symmetry.

Findings

SU(N) topological phases can be stabilized at half-filling

Even N yields the spin-1 Haldane phase without symmetry breaking

For N=3, chiral Haldane phases with boundary degeneracy emerge

Abstract

We propose to realize one-dimensional topological phases protected by SU($N$) symmetry using alkali or alkaline-earth atoms loaded into a bichromatic optical lattice. We derive a realistic model for this system and investigate it theoretically. Depending on the parity of $N$, two different classes of symmetry-protected topological (SPT) phases are stabilized at half-filling for physical parameters of the model. For even $N$, the celebrated spin-1 Haldane phase and its generalization to SU($N$) are obtained with no local symmetry breaking. In stark contrast, at least for $N=3$, a new class of SPT phases, dubbed chiral Haldane phases, that spontaneously break inversion symmetry, emerge with a two-fold ground-state degeneracy. The latter ground states with open-boundary conditions are characterized by different left and right boundary spins which are related by conjugation. Our results show that topological phases are within close reach of the latest experiments on cold fermions in optical lattices.