Emergent topological re-entrant phase transition in a generalized quasiperiodic modulated Su-Schrieffer-Heeger model

We study the topological properties of the one-dimensional generalized quasiperiodic modulated Su-Schrieffer-Heeger model. The results reveal that the topological re-entrant phase transition emerges. Through the analysis of a real-space winding number, we divide the emergent topological re-entrant phase transitions into two types. The first is the re-entrant phase transition from the traditional topological insulator phase into the topological Anderson insulator phase, and the second is the re-entrant phenomenon from one topological Anderson insulator phase into another topological Anderson insulator phase. These two types of re-entrant phase transitions correspond to bounded and unbounded cases of quasiperiodic modulation, respectively. Furthermore, we verify the above topological re-entrant phase transitions by analyzing the Lyapunov exponent and bulk gap. Since Su-Schrieffer-Heeger models have been realized in various artificial systems (such as cold atoms, optical waveguide arrays, ion traps, Rydberg atom arrays, etc.), the two types of topological re-entrant phase transitions predicted in this paper are expected to be realized in the near future.