Novel transition between critical and localized states in a one-dimensional quasiperiodic system

We study a one-dimensional tight-binding model, where site energies are given by ${\varepsilon }_k$=V cos2π${\mathrm{fx}}_k$, with $x_k$ denoting the kth quasiperiodic lattice site. It is found that there exists critical states when 2πf corresponds to a reciprocal lattice vector of the quasiperiodic lattice. For other values of f, critical and localized states are coexistent for V$V_c$=1.361±0.001, while all states are loalized for V>$V_c$; there is a transition between them at V=$V_c$. As the critical point is approached from the localized states, the localization length diverges with a critical exponent β≃2.0. .AE