  We present a Green's function formalism to investigate the topological
properties of weakly interacting one-dimensional topological insulators,
including the bulk-edge correspondence and the quantum criticality near
topological phase transitions, and using interacting Su-Schrieffer-Heeger model
as an example. From the many-body spectral function, we find that closing of
the bulk gap remains a defining feature even if the topological phase
transition is driven by interactions. The existence of edge state in the
presence of interactions can be captured by means of a T-matrix formalism
combined with Dyson's equation, and the bulk-edge correspondence is shown to be
satisfied even in the presence of interactions. The critical exponent of the
edge state decay length is shown to be affiliated with the same universality
class as the noninteracting limit.
