Non-local spin correlation as a signature of Ising anyons trapped in vacancies of the Kitaev spin liquid

Abstract

In the Kitaev chiral spin liquid, Ising anyons are realized as $Z_2$ fluxes binding Majorana zero modes, which, however, are thermal excitations with finite decay rates. On the other hand, a lattice vacancy traps a $Z_2$ flux even in the ground state, resulting in the stable realization of a Majorana zero mode in a vacancy. We demonstrate that spin-spin correlation functions between two vacancy sites exhibit long-range correlation arising from the fractionalized character of Majorana zero modes, in spite of the strong decay of bulk spin correlations. Remarkably, this non-local spin correlation does not decrease as the distance between two vacancy sites increases, signaling Majorana teleportation. Furthermore, we clarify that the non-local correlation can be detected electrically via the measurement of non-local conductance between two vacancy sites, which is straightforwardly utilized for the readout of Majorana qubits. These findings pave the way to the measurement-based quantum computation with Ising anyons trapped in vacancies of the Kitaev spin liquid.

6 pages + 4 figures, and Supplemental Material

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Cited by in corpus (10)

• Kitaev Quantum Spin Liquids
• Defect-Induced Low-Energy Majorana Excitations in the Kitaev Magnet $\alpha$-RuCl${}_3$
• Field-driven spatiotemporal manipulation of Majorana zero modes in a Kitaev spin liquid
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