Trace map of a general aperiodic Thue-Morse chain: Electronic properties

We develop an analytical method, using a real-space renormalization-group technique, for calculating the trace maps of quasiperiodic or aperiodic substitutional sequences. This method is quite different from the standard method of calculating the trace map from the recursion relation of the transfer matrices. The standard procedure solely depends on the unimodular property of the transfer matrices, but in the present method it is possible to find the trace-map equations for many physical models where the transfer matrices may or may not be unimodular. In this paper we take the general Thue-Morse lattice, as a typical example, to illustrate our method, and solve the trace-map equations exactly under periodic boundary conditions for studying the electronic spectrum and its local scaling indices. [S0163-1829(98)00829-7].