Density of states of two dimensional quasiperiodic lattices in the thermodynamic limit

Abstract

A scheme based on real-space renormalization group method to find density of states of two dimensional lattices in the thermodynamic limit is introduced in this paper. The main importance of this method is its applicability in two dimensional quasiperiodic systems for which no analytic solution is possible. Previously there were many works with real-space renormalization scheme in one dimensional lattices, but its application in two dimensional systems was not successful. In the present scheme, we have mapped the two dimensional system into a number of one dimensional systems, and applying real-space renormalization method to those new one dimensional systems we have found out the density of states of the entire two dimensional system.