3 research outputs found
Hidden dimers and the matrix maps: Fibonacci chains re-visited
The existence of cycles of the matrix maps in Fibonacci class of lattices is
well established. We show that such cycles are intimately connected with the
presence of interesting positional correlations among the constituent `atoms'
in a one dimensional quasiperiodic lattice. We particularly address the
transfer model of the classic golden mean Fibonacci chain where a six cycle of
the full matrix map exists at the centre of the spectrum [Kohmoto et al, Phys.
Rev. B 35, 1020 (1987)], and for which no simple physical picture has so far
been provided, to the best of our knowledge. In addition, we show that our
prescription leads to a determination of other energy values for a mixed model
of the Fibonacci chain, for which the full matrix map may have similar cyclic
behaviour. Apart from the standard transfer-model of a golden mean Fibonacci
chain, we address a variant of it and the silver mean lattice, where the
existence of four cycles of the matrix map is already known to exist. The
underlying positional correlations for all such cases are discussed in details.Comment: 14 pages, 2 figures. Submitted to Physical Review