A Renormalization Analysis of One-Dimensional Thue-Morse Lattice

The one-dimensional Thue-Morse sequence with a generating matrix of determinant zero has been suggested to be intermediate between a periodic structure and a standard quasiperiodic structure like the Fibonacci sequence. The renormalization procedure developed in our previous study of one-dimensional Fibonacci quasicrystal is here applied to discuss the electronic spectrum of a tight-binding Thue-Morse quasicrystal. The resulting integrated electronic density of states shows indeed, a structure which is more like that of a periodic chain than a Fibonacci quasicrystal. We suggest the analytical procedure can be extended to study one-dimensional quasicrystals of any other kind, the two-dimensional Penrose lattice as well as three-dimensional real quasicrystals.