Correspondence between a shaken honeycomb lattice and the Haldane model

TL;DR

This paper explores the relationship between a periodically modulated honeycomb lattice and the Haldane model, revealing that while they share topological phases, their Hamiltonians differ significantly, with the shaken lattice exhibiting a richer structure.

Contribution

It demonstrates that the shaken honeycomb lattice's Floquet Hamiltonian is not equivalent to the Haldane model, despite sharing the same topological phase diagram.

Findings

Shared topological phase diagram between systems

Differences in Hamiltonian structures

Shaken lattice has a richer Hamiltonian structure

Abstract

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 [Jotzu et al., Nature 515, 237 (2014)] - the corresponding Hamiltonians are not equivalent, the one of the shaken lattice presenting a much richer structure.