Topological transitions of interacting bosons in one-dimensional bichromatic optical lattices

Ultracold atoms in one-dimensional (1D) bichromatic optical lattices constitute a surprisingly simple system for the study of topological insulators. We show that bosons in 1D bichromatic lattices present as a general feature the existence, at equal fractional filling, of Mott-insulator phases with different topological character. These different phases are a direct consequence of the bosonic and interacting nature of the particles and the topological nature of the Bloch bands. We demonstrate that the associated hidden topological transitions may occur both as a function of the superlattice strength and due to intersite interactions. We also discuss the topological character of incommensurate density-wave phases in quasiperiodic superlattices.