For irrational values of β β , corresponding to a modulation of the onsite energy incommensurate with the underlying lattice, the model exhibits a quantum phase transition between a metallic phase and an insulating phase as λ λ is varied. For example, for β β = ( 1 + 5 ) / 2 (the golden ratio) and almost any φ φ , if λ λ > 2 J the eigenmodes are exponentially localized, while if λ λ < 2 J the eigenmodes are extended plane waves. The Aubry-André metal-insulator transition happens at the critical value of λ λ which separates these two behaviors, λ λ = 2 J .