  Topological crystalline insulators are phases of matter where the crystalline
symmetries solely protect the topology. In this work, we explore the effect of
many-body interactions in a subclass of topological crystalline insulators,
namely the mirror-symmetry protected topological crystalline insulator.
Employing a prototypical mirror-symmetric quasi-one-dimensional model, we
demonstrate the emergence of a mirror-symmetry protected topological phase and
its robustness in the presence of short-range interactions. When longer-range
interactions are introduced, we find an interaction-induced topological phase
transition between the mirror-symmetry protected topological order and a
trivial charge density wave. The results are obtained using density-matrix
renormalization group and quantum Monte-Carlo simulations in applicable limits.
