Correspondence between a shaken honeycomb lattice and the Haldane model

We investigate the correspondence between the tight-binding Floquet Hamiltonian of a periodically modulated honeycomb lattice and the Haldane model. We show that—though the two systems share the same topological phase diagram, as reported in a breakthrough experiment with ultracold atoms in a stretched honeycomb lattice [G. Jotzuet al., Nature (London) 515,237(2014)]—the corresponding Hamiltonians are not equivalent, the one of the shaken lattice presenting a much richer structure.