Wave function behavior in a Fibonacci lattice with electronic correlation

The electronic correlation and the spatial symmetry in quasicrystals are by themselves two very complicated research topics since we cannot use the reciprocal space to study quasicrystals and the electronic correlation in many-body system has been solved exactly only for one and for infinite dimension. We should note that even in one-dimensional quasiperiodic structures, the interactions between electrons have often been neglected and only few results have been obtained. In this work, we solved the case of two interacting particles in a Fibonacci lattice using a real-space method and the Hubbard model. The real-space method is based on mapping the correlated many-body problem onto an equivalent site- and bond-impurity tight-binding one in a higher dimensional space. Within the Hubbard Hamiltonian we obtained the behavior of the wave function and the analysis of these eigen-functions in the Fibonacci lattice when correlation is off shows a critical behavior.