Quantum Heisenberg-Ising models on generalized Fibonacci lattices

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Abstract
We study the quantum Heisenberg-Ising models on generalized Fibonacci lattices by the dynamical-maps technique, in which the nearest-neighbor Ising interactions take two values that follow successively the generalized Fibonacci sequences. The energy spectra are Cantor-like, and the wave functions are generally critical. It is further shown that the energy spectra do not have uniform scalings and that for some systems the wave functions are extended or localized in certain energy regions. In addition, we also obtain the critical lines of the quasiperiodic quantum Heisenberg-Ising models.