  The interacting SSH model provides an ideal ground to study the interplay
between topologically insulating phases and electron-electron interactions. We
study the polarization density as a topological invariant and provide an
analytic treatment of its behavior in the low-energy sector of the
one-dimensional interacting SSH model. By formulating the topological invariant
in terms of Green's functions, we use the low-energy field theory of the
Thirring model to derive the behavior of the polarization density. We show that
the polarization density in the continuum theory describes the usual
topological insulating phases. Still, it contains an extra factor from the
fields' scaling dimensions in the low-energy quantum field theory. We interpret
this as a measure of the modified charge of the new excitations in the system.
We find two distinct contributions: a renormalization of the electronic charge
$e$ of a Fermi liquid because of quasiparticle smearing and an additional
contribution coming from the topological charge of the soliton arising in the
bosonized version of the Thirring model, the sine-Gordon model.
