Distinct trivial phases and topological transitions in an interpolating Aubry-André-Fibonacci p-wave superconducting chain

We investigate the topological properties and their evolution with the interpolation parameter in a generalized interpolating Aubry−Andr´e−Fibonacci (IAAF) model with p-wave superconducting pairing. Analytical phase boundaries are derived for both the AA and Fibonacci limits. In the AA limit, the system undergoes a transition from a topologically nontrivial superconducting phase to an Anderson-localized trivial phase, while in the Fibonacci limit, it evolves into a topologically trivial superconducting phase composed of multifractal critical states that are extended but non-ergodic. These two trivial phases are thus physically distinct. As the interpolation parameter increases, analytical predictions gradually deviate from numerical results due to the structural change of the chemical potential from a smooth cosine to a discrete step-like modulation. Using the dualspace criterion, we demonstrate that the intermediate regime is not a genuine critical phase but a smooth crossover. Remarkably, near the Fibonacci limit, the phase boundary becomes robust against further increases of the interpolation parameter, demonstrating the protective role of Fibonacci quasiperiodicity. Our results establish a comprehensive theoretical framework for topological phase transitions in interpolated quasiperiodic systems.