Renormalization Group on the Aperiodic Hamiltonian

We present the renormalization group of the generalized Fibonacci lattices associated with the aperiodic sequences as constructed by the inflation rule: A,B →AⁿB^m,A, in which m and n are positive integers. The derived renormalization group consists of 2n(n+ m - 1) + 1 basic renormalization-group Mtransformations. By suitable combinations of these basic transformations, the local electronic properties of the generalized Fibonacci lattices can be exactly obtained.