On the non-hermitian Kitaev chain

Abstract: We study the non-hermitian Kitaev chain model, for arbitrary complex parameters. In particular, we give a concise characterisation of the curves of eigenvalues in the complex plane in the infinite size limit, using a novel method which can be applied to other non-hermitian systems. Using this solution, we characterise under which conditions the skin effect is absent, and for which eigenstates this is the case. We also fully determine the region in parameter space for which the model has a zero mode.