We study the multifractal criticality in a generalized Su-Schrieffer-Heeger model. The results show that the system supports not only critical phases but also reentrance multifractalization (REM). By mapping the hopping term to an effective potential, we analytically prove that although the model has no explicit unbounded potential, a hidden unbounded potential is actually present—this is the key mechanism driving the emergence of multifractal critical phases. Moreover, one can get a condition where the competition between the explicit and hidden unbounded potentials is exactly balanced. Under this condition, the multifractal critical phase vanishes, and the system returns to the extended phase. Based on this mechanism, we achieve both demultifractalization and reentrant multifractalization. Finally, we double-check the theoretical predictions through wave packet dynamics, and the numerical results are consistent with our theoretical analysis. This work broadens our understanding of how unbounded potentials induce multifractal critical phases, providing a theoretical basis for designing new systems with multifractal critical phases.

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• Anderson localization
• 1-dimensional systems
• Disordered systems
• Quasicrystals