Analytical solution for pairing of two-particles in a quasiperiodic lattice within the Hubbard model

In this work we solve the generalized Hubbard model for two-interacting particles in a Fibonacci infinite one-dimensional lattice, using a real-space mapping method, the renormalized perturbation expansion and the Green function technique. The real-space method is based on mapping the correlated many-body problem onto an equivalent site- and bond-impurity tight-binding problem in a higher dimensional space. Analyzing the quasiperiodic lattice in this new space we obtained an approximate analytical solution for the binding condition at the ground state. Our results reproduce the limit case, that is, the periodic lattice.