Wavefunctions and correlations of the complex Kitaev model on a finite chain

In this thesis, we discuss the Kitaev model, a one-dimensional topological superconductor. In the non-trivial phase, it shows two Majorana edge states that can be combined, in the thermodynamic limit, into a non-local zero-energy Dirac fermion which can be populated without affecting the energy of the states. In this work, we find the analytical expressions of the Majorana edge states for finite chain length and some extension of the model. In particular, we consider generic boundary conditions and complex-valued parameters. In order to do this, we extend the Lieb-Schultz-Mattis method to the fully complex case. Then we discuss the splitting of the degeneracy of the ground state for finite systems and the emergence of the massive edge states. Finally, we calculate the entanglement entropy of the complex Kitaev model from the correlation functions by proposing an extension of the standard real method to the complex case.