We study the topological properties of a one-dimensional quasiperiodic-potential-modulated mosaic trimer lattice. To begin with, we first investigate the topological properties of the model in the clean limit free of quasiperiodic modulation based on analytical derivations and numerical calculations of the Zak phase $Z$ and the polarization $P$. Two nontrivial topological phases corresponding to $1/3$ filling and $2/3$ filling, respectively, are revealed. Then we incorporate the mosaic modulation and investigate the influence of quasiperiodic modulation on the two existing topological phases. Interestingly, it turns out that quasiperiodic modulation gives rise to multiple distinct effects for different fillings. At $2/3$ filling, the topological phase is significantly enhanced by the quasiperiodic modulation, where a topologically trivial region adjacent to the original topological phase is converted into a topological one. Based on the calculations of polarization and the relevant level spacing, we explicitly present a corresponding topological phase diagram in the $\lambda \text{−}J$ plane. While for the $1/3$ filling case, the quasiperiodic modulation dramatically compresses the topological phase, and strikingly, further induces the emergence of reentrant topological phase transitions instead. Furthermore, we verify the topological phase diagrams by computing the many-body ground-state fidelity susceptibility for both the $1/3$ filling and the $2/3$ filling cases. Our work exemplifies the diverse roles of quasiperiodic potential in the modulation of topological properties, and will further inspire more research on the competitive and cooperative interplay between topological properties and quasiperiodic modulations.

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• Topological insulators
• Topological phase transition
• Disordered systems
• Random & disordered media
• Lattice models in condensed matter