Abstract

The realization of the Hofstadter model in a strongly anisotropic ladder geometry has now become possible in one-dimensional optical lattices with a synthetic dimension. In this talk, I discuss how the Hofstadter Hamiltonian in such ladder configurations hosts a topological phase of matter which is radically different from its two-dimensional counterpart. This topological phase stems directly from the hybrid nature of the ladder geometry, and is protected by a properly defined inversion symmetry. I will consider the paradigmatic case of a three-leg ladder which supports a topological phase exhibiting the typical features of topological states in one dimension: robust fermionic edge modes, a degenerate entanglement spectrum and a non-zero Zak phase; then, I will generalize my results to ladders with an higher number of legs which are addressable in the state-of-the-art cold atom experiments.