Interplay between topology and interactions in superconducting chains

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