TRACE MAP OF A GENERAL APERIODIC THUE-MORSE CHAIN - ELECTRONIC-PROPERTIES

We develop an analytical method, using a real-space renormalization-gr oup technique, for calculating the trace maps of quasiperiodic or aper iodic substitutional sequences. This method is quite different from th e standard method of calculating the trace map from the recursion rela tion of the transfer matrices. The standard procedure solely depends o n the unimodular property of the transfer matrices, but in the present method it is possible to find the trace-map equations for many physic al models where the transfer matrices may or may not be unimodular. In this paper we take the general Thue-Morse lattice, as a typical examp le, to illustrate our method, and solve the trace-map equations exactl y under periodic boundary conditions for studying the electronic spect rum and its local scaling indices. [S0163-1829(98)00829-7].