Interplay between topology and interactions in superconducting chains

Most studies on non-trivial topological systems have been carried out using non-interacting models that admit an exact solution. This raises the question of the, extent to which the consideration of electronic correlations and disorder, present in real systems, modifies these results. Exact solutions for correlated electronic systems with non-trivial topological properties, although fundamental are scarce. Among the non-interacting solvable models, we single out the Kitaev p-wave superconducting chain. It plays a crucial role in clarifying the appearance of emergent quasi-particles, that is, the Majorana modes, associated with non-trivial topological properties. Given the relevance of this model, it would be extremely useful if it could be extended to include correlations and remain solvable. In this work we investigate a superconducting Kitaev chain that interacts through a Falicov-Kimball Hamiltonian with a background of localized electrons. This model can be solved exactly for relevant values of its parameters, by mapping it into a non-interacting one. This allows for a detailed study of the interplay between electronic correlations and non- trivial topological behavior. In addition, the random occupation of the chain by local moments brings new interesting effects associated with disorder.