Anatomy of two-body-propagator topology

One convenient way to define topological quantum numbers for interacting topological insulators, is to directly analyze the single-particle propagator. Here, we extend this idea to two-body propagators, which characterize both bound and scattering states of two topological particles interacting via short-ranged interactions. Based on explicit examples, we show how to define topological quantum numbers even if the bound state bands have entered the scattering continuum. This allows to go beyond the commonly-assumed strong-coupling limit. We comment on topological phase transitions and the bulk-boundary correspondence in the two-body case.