  We propose an efficient scheme for simulating the topological phases of
matter based on silicon-vacancy (SiV) center arrays in phononic crystals. This
phononic band gap structure allows for long-range spin-spin interactions with a
tunable profile. Under a particular periodic microwave driving, the band-gap
mediated spin-spin interaction can be further designed with the form of the
Su-Schrieffer-Heeger (SSH) Hamiltonian. In momentum space, we investigate the
topological characters of the SSH model, and show that the topological
nontrivial phase can be obtained through modulating the periodic driving
fields. Furthermore, we explore the zero-energy topological edge states at the
boundary of the color center arrays, and study the robust quantum information
transfer via the topological edge states. This setup provides a scalable and
promising platform for studying topological quantum physics and quantum
information processing with color centers and phononic crystals.
