Localization as a consequence of quasiperiodic bulk-bulk correspondence

We report on a direct connection between band theory, quasiperiodic topology, and the almost-Mathieu (Aubry-Andre) metal insulator transition (MIT). By constructing the transfer matrix equations of onedimensional (1D) quasiperiodic operators from rational approximate projected Green's functions, we relate the quasiperiodic Lyapunov exponents to the chiral edge modes of rational-flux Hofstadter Hamiltonians. We thereby show that the insulating phase is rooted in a topological "bulk-bulk" correspondence, a bulk-boundary correspondence between the 1D Aubry-Andre system (boundary) and its two-dimensional (2D) parent Hamiltonian (bulk). We extend this connection to random disorder via a Fourier expansion in quasiperiodic modes, demonstrating our results are widely applicable to systems beyond this paradigmatic model. The uncorrelated disorder limit is characterized by the breakdown of bulk-boundary driven quasiperiodic localization.