Interaction-driven phase transition in one dimensional mirror-symmetry protected topological insulator

Topological crystalline insulators are phases of matter where the crystalline symme-tries solely protect the topology. In this work, we explore the effect of many-body inter-actions 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 pro-tected topological phase and its robustness in the presence of short-range interactions. When longer-range interactions are introduced, we find an interaction-induced topolog-ical phase transition between the mirror-symmetry protected topological order and a trivial charge density wave. The results are obtained using density-matrix renormaliza-tion group and quantum Monte Carlo simulations in applicable limits.