  In this work, we study a one-dimensional model of interacting bosons coupled
to a dynamical $\mathbb{Z}_2$ field, the $\mathbb{Z}_2$ Bose-Hubbard model, and
analyze the interplay between spontaneous symmetry breaking and topological
symmetry protection. In a previous work, we showed how this model exhibits a
spontaneous breaking of the translational symmetry through a bosonic Peierls
transition. Here we find how, at half filling, the resulting phase also
displays topological features that coexist with the presence of long-range
order and yields a topological bond order wave. Using both analytical and
numerical methods, we describe the properties of this phase, showing that it
cannot be adiabatically connected to a bosonic topological phase with vanishing
Hubbard interactions, and thus constitutes an instance of an
interaction-induced symmetry-breaking topological insulator.
