Few particles correlation in a one-dimensional quasiperiodic lattice

During the last two decades, two of the most important discoveries in condensed matter physics have been the discovery of quasicrystals and the discovery of high-Tc ceramic superconductors. These topics have generated a large number of experimental and theoretical studies in the physics of low dimension. They have also modified some of the concepts in solid state physics. For instance, it was believed that the five-fold symmetry was incompatible with a long-range order and it was not expected that ceramic materials with a high-Tc and a short coherence length exhibit superconductivity. Therefore, it is important to revise both the spatial symmetry and the electronic correlation to identify how they affect the physical properties of materials. The study of these subjects is complex since we cannot use the reciprocal space to study quasicrystals and the electronic correlation in many-body systems has not entirely been solved. 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 cases of two and three interacting particles in a Fibonacci lattice using a real-space method, the Green function technique, the renormalized perturbation expansion method and the Hubbard model. For the case of two interacting particles an analytical solution for the pairing phase diagram was obtained using the extended Hubbard Hamiltonian. For the case of three interacting particles the binding energy was numerically calculated. The results present here are compared with those obtained for the periodic and binary lattices.