Majorana states in inhomogeneous spin ladders

TL;DR

This paper introduces an inhomogeneous spin ladder model related to the Kitaev model, demonstrating the stability and braiding of Majorana end states under various perturbations, offering a potential platform for topological quantum computation.

Contribution

It proposes a tunable inhomogeneous spin ladder system that supports stable Majorana states and demonstrates their braiding capabilities, advancing topological quantum computing research.

Findings

Majorana end states are robust against two-body perturbations in inhomogeneous ladders.

Inhomogeneous magnetic fields do not destroy topological degeneracy.

A trijunction setup enables braiding of Majorana states.

Abstract

We propose an inhomogeneous open spin ladder, related to the Kitaev honeycomb model, which can be tuned between topological and nontopological phases. In extension of Lieb's theorem, we show numerically that the ground state of the spin ladder is either vortex free or vortex full. We study the robustness of Majorana end states (MES) which emerge at the boundary between sections in different topological phases and show that while the MES in the homogeneous ladder are destroyed by single-body perturbations, in the presence of inhomogeneities at least two-body perturbations are required to destabilize MES. Furthermore, we prove that x, y, or z inhomogeneous magnetic fields are not able to destroy the topological degeneracy. Finally, we present a trijunction setup where MES can be braided. A network of such spin ladders provides thus a promising platform for realization and manipulation of MES.