Mapping topology-disorder phase diagram with a quantum simulator

We explore the topology-disorder phase diagram by simulating one-dimensional Su-Schrieffer-Heeger (SSH) model with quasiperiodic disorder using a programmable superconducting simulator. We experimentally map out and identify various trivial and topological phases with extended and localized bulk states. We find that in the topological phase the bulk states can be critically localized without mobility edge or contain both critically and completely localized states. In addition, there exist trivial and topological intermediate phases with mobility edge and coexistence of extended and completely localized states. The presence of the surprisingly rich phases in the simple SSH model with quasiperiodic disorder sheds new light on the investigation of the topological and localization phenomena in condensed-matter physics.