| We study the properties of a parity- and time-reversal- (PT) symmetric tight-binding chain of size N with position-dependent hopping amplitude. In contrast to the fragile PT-symmetric phase of a chain with constant hopping and imaginary impurity potentials, we show that, under very general conditions, our model is {\it always} in the PT-symmetric phase. We numerically obtain the energy spectrum and the density of states of such a chain, and show that they are widely tunable. We show that the Hermitian counterpart of such a chain can be realized in coupled waveguides with a non-uniform hopping, and present results for photon dispersion, localization, and correlations in such waveguides. |
|