Manipulating unpaired Majorana fermions in a quantum spin chain

Abstract

We analyze an exactly solvable spin-1/2 chain which is a generalized version of Kitaev's honeycomb model. We show that every state of the system has a ${2}^{N/4}$-fold degeneracy, where $N$ is the number of sites. We present analytic solutions for the zero energy modes of the Majorana fermions. Localized, unpaired Majorana modes occur even in the bulk of the chain and they are bound to kink (antikink) ${Z}_{2}$ flux configurations. The unpaired Majorana modes can therefore be created and manipulated if the ${Z}_{2}$ flux configurations can be controlled. We delineate the regions in parameter space for homogenous chains where the zero modes occur. We further show that there is a large parameter space for inhomogenous chains where the unpaired modes occur and that their wave functions can be tuned if the couplings of the model can be tuned.