Quantum simulation of topological phases and transitions

Since the discovery of topological phases and materials, topology, as a mathematical concept, has inspired great interest in modern condensed matter physics. Although manytypes of topological materials have been predicted and discovered, their simulation in controllable artificial quantum systems will greatly help our understanding and further study of such materials, and various experimental methods have already been developed. In this paper we briefly summarizethe progress of quantum simulation in cold atoms and superconducting qubit systems. We describe the characteristics of different quantum systems and the corresponding experimental methods for their simulation. In addition, we also summarize the relationship between the experimental schemes and physical principles of the two systems.