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

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