Eigenstate Transitions, Duality, and Anomalous Diffusion in a Quasiperiodic Qi-Wu-Zhang Chern Insulator

Quasiperiodic systems usually interpolate between extended, critical, and localized states as the quasiperiodic modulation is increased. Here we show that the magnetic Qi-Wu-Zhang Chern-insulator model realizes a distinct full-spectrum transition in which localization is avoided. For an irrational magnetic flux, the two-dimensional model reduces to a spinor quasiperiodic chain with a matrix onsite modulation controlled by the hopping amplitude $t_x$. When $|m+2|>t_y$, increasing $t_x$ produces the conventional extended-critical-localized sequence with a critical line at $t_x=t_y$. In contrast, when $|m+2|\le t_y$, the system changes from an extended phase to a critical phase at $t_x=|m+2|$ and remains critical even for stronger quasiperiodic modulation. Finite-size scaling of the average inverse participation ratio gives $\overline{\mathrm{IPR}}\sim q^{-\alpha}$ with $0<\alpha<1$ throughout this persistent critical regime. A dual transformation exchanging $t_x$ and $t_y$, together with a Lyapunov-exponent analysis, explains the phase diagram. Wave-packet dynamics further distinguish ballistic, anomalous-diffusive, and localized regimes. These results identify magnetic Chern-insulator systems as a natural platform for robust criticality and anomalous quantum transport.