We develop a renormalization group (RG) description of the localization properties of one-dimensional (1D) quasiperiodic lattice models. The RG flow is induced by increasing the unit cell of subsequent commensurate approximants. Phases of quasiperiodic systems are characterized by RG fixed points associated with renormalized single-band models. We identify fixed points that include many previously reported exactly solvable quasiperiodic models. By classifying relevant and irrelevant perturbations, we show that the phase boundaries of more generic models can be determined with exponential accuracy in the approximant's unit cell size, and in some cases analytically. Our findings provide a unified understanding of widely different classes of 1D quasiperiodic systems.

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• Anderson localization
• Localization
• 1-dimensional systems
• Disordered systems
• Renormalization group