Finite-size effects of the spinless long-range BCS Kitaev chain

Kurzfassung

Topological phases in superconductors are of great interest due to their potential use for topological quantum computing. They are usually characterized by quasiparticles located at the edges of the superconductor. We investigate how long-range interactions affect the properties of the well-known Kitaev chain, which is solved self-consistently with the mean-field approximation. We find that for weak interactions, the Majorana edge modes have finite energy that decay algebraically to zero with the long-range power law. Strong long-range interactions are a special case due to their slow decay. The solution of the thermodynamic limit without finite-size effects is a local minimum to this problem, but with a larger ground-state energy in contrast to the discussed solution. Our results show the difference between the self-consistent and the Kitaev approach, which has clear constraints on long-range interactions.