Jovan Odavić: Simulating semi-infinite generalized Aubry-André-Harper model using continued fractions

Using continued fractions and recurrence relations for the corresponding convergents we derive an expression for the reservoir self-energy which enables numerical simulation of the semi-infinite generalized Aubry-André-Harper (AAH) model with finite periodicity within the Green’s functions formalism. To demonstrate the effectiveness of the derived expression we compute the local and total density of states, density per lattice site, and examine the existence of a phase transition using Inverse Participation Ratio (IPR) in the thermodynamic limit. Furthermore, we discuss the possibility of the identification of topological regimes within the periodic hopping lattice models using the exact reservoir self-energy expression.