Manipulating unpaired Majorana fermions in a quantum spin chain

TL;DR

This paper analyzes an exactly solvable spin-1/2 chain model, revealing the presence of localized unpaired Majorana modes bound to flux configurations, with potential for manipulation through parameter tuning.

Contribution

It provides analytic solutions for zero energy Majorana modes in a generalized Kitaev chain, including conditions for their existence and tunability in both homogeneous and inhomogeneous systems.

Findings

Unpaired Majorana modes occur in the bulk of the chain.

Zero energy modes are bound to $Z_2$ flux configurations.

Majorana wavefunctions can be tuned via coupling parameters.

Abstract

We analyse an exactly solvable spin-$1/2$ chain which is a generalised 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. Localised, unpaired Majorana modes occur even in the bulk of the chain and they are bound to kink (anti-kink) $Z_2$ flux configurations. The unpaired Majorana modes can therefore be created and manipiulated 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 wavefunctions can be tuned if the couplings of the model can be tuned.