Topological transitions of interacting bosons in one-dimensional bi-chromatic optical lattices

Ultra-cold atoms in 1D bi-chromatic lattices constitute a surprisingly simple system for the study of topological insulators. We show that topological phase transitions constitute a general feature of bosons in 1D bi-chromatic lattices, and that these transitions may occur both as a function of the superlattice strength and due to inter-site interactions. We discuss in addition the topological character of incommensurate density wave phases in quasi-periodic lattices.