Simulation of topological Zak phase in spin-phononic crystal networks

Abstract

Topological states of matter are particularly interesting for both fundamental research and practical applications. Simulating topological phases in a quantum system is of great interest due to the ability to explore a plethora of topologically nontrivial phenomena in a controllable fashion. We propose and analyze an efficient scheme for simulating topological Zak phase in two-dimensional spin-phononic crystal networks. We show that through a specially designed periodic driving, one can selectively control and enhance the bipartite silicon-vacancy center arrays, so as to obtain chiral-symmetry-protected spin-spin couplings. More importantly, the Floquet engineering spin-spin interactions support rich quantum phases associated with topological invariants. In momentum space, we analyze and simulate the topological nontrivial properties of the one- and two-dimensional systems. As an application in quantum information processing, we study the robust quantum state transfer via topologically protected edge states. This work opens up new prospects for studying quantum acoustics and offers an experimentally feasible platform for the study of topological phases of matter.