Invariable mobility edge in a quasiperiodic lattice

We analytically and numerically study a 1D tight-binding model with tunable incommensurate potentials. We utilize the self-dual relation to obtain the critical energy, namely, the mobility edge. Interestingly, we analytically demonstrate that this critical energy is a constant independent of strength of potentials. Then we numerically verify the analytical results by analyzing the spatial distributions of wave functions, the inverse participation rate and the multifractal theory. All numerical results are in excellent agreement with the analytical results. Finally, we give a brief discussion on the possible experimental observation of the invariable mobility edge in the system of ultracold atoms in optical lattices.