The Haldane Model with Chiral Edge States using a Synthetic Dimension

We explicitly show that the differences, with respect to the appearance of topological phases, between the traditional Haldane model, which utilises a honeycomb lattice structure, to that of the Haldane model imbued onto a brick-wall lattice geometry, are inconsequential. A proposal is then put forward to realise the Haldane model by exploiting the internal degrees of freedom of atoms as a synthetic dimension. This leads to a convenient platform for the investigation of chiral edge states due to the hard boundaries provided by the hyperfine manifold. We make some cursory comments on the effects of interactions in the system.