Parity order as a fundamental driver of bosonic topology

Abstract: Symmetry-protected topological (SPT) phases in interacting bosonic systems have been extensively studied, yet most realizations rely on fine-tuned interactions or enlarged symmetries. Here we show that a qualitatively different mechanism--parity order coupled to bond dimerization--acts as a fundamental driver of bosonic topology. Using density matrix renormalization group simulations, we identify two distinct topological phases absent in the purely dimerized model: an SPT phase at half filling stabilized by positive parity coupling, and a topological phase at unit filling stabilized by negative coupling that can be adiabatically connected to a trivial phase without breaking any symmetry. Our results establish parity order as a new organizing principle for correlation-driven bosonic topology.