Real-space rescaling method for the spectral properties of tight-binding systems

Exact real-space rescaling transformations are used to calculate the spectral properties of tight-binding Hamiltonians with arbitrary range of interaction on a linear chain. Singularities of the spectral functions within the band of extended states are associated with fixed points of the rescaling transformation. The fixed points separate regions of energy in which the behavior of the system is qualitatively different. The method is not restricted to one dimension and can also be used to treat single-impurity problems.