An exact systematized renormalization-group approach for periodic and aperiodic systems

Abstract

A systematized renormalization-group approach is present to study systematically the physical properties of the one-dimensional systems arranged in the 1D sequence which are constructed by the inflation rule (A,B) to )Am11Bm12, Bm21Am22). A basic decimation rule is introduced, which is intuitive, simplified and exact, to investigate the electronic properties of the systems which contain crystals and quasicrystals. As typical examples, the spectra of global electronic bands of the 1D systems with (m11,m12,m21,m22)=(1,1,0,1). (1,1,1,1), and (1,1,2,1) are numerically calculated.