  The Su-Schrieffer-Heeger chain is a prototype example of a symmetry-protected
topological insulator. Coupling it non-perturbatively to local thermal
environments, either through the intercell or the intracell fermion tunneling
elements, modifies the topological window. To understand this effect, we employ
the recently developed reaction-coordinate polaron transform (RCPT) method,
which allows treating system-bath interactions at arbitrary strengths. The
effective system Hamiltonian, which is obtained via the RCPT, exposes the
impact of the baths on the SSH chain through renormalization of tunneling
elements and the generation of many-body interaction terms. By performing exact
diagonalization and computing the ensemble geometric phase, a topological
invariant applicable even to systems at finite temperature, we distinguish the
trivial band insulator (BI) from the topological insulator (TI) phases.
Furthermore, through the RCPT mapping, we are able to pinpoint the main
mechanism behind the extension of the parameter space for the TI or the BI
phases (depending on the coupling scheme, intracell or intercell), which is the
bath-induced, dimerized, many-body interaction. We also study the effect of
on-site staggered potentials on the SSH phase diagram, and discuss extensions
of our method to higher dimensions.
