Majorana-assisted nonlocal spin correlation in quasi-one-dimensional Kitaev spin liquids

TL;DR

This paper demonstrates that Majorana zero modes in quasi-1D Kitaev spin liquids lead to observable nonlocal spin correlations, providing a concrete signature of Majorana nonlocality in quantum spin liquids.

Contribution

It reveals how Majorana zero modes induce nonlocal spin correlations in quasi-1D Kitaev models, linking Majorana nonlocality to measurable spin-string operators.

Findings

Finite nonlocal spin correlation confirmed numerically.

Majorana zero modes produce end-to-end spin correlations.

Nonlocal correlations occur without local magnetization.

Abstract

We propose Majorana-assisted nonlocal spin correlation as a manifestation of Majorana nonlocality in quasi-one-dimensional (1D) Kitaev spin liquids. Focusing on the flux-free sector of the Kitaev honeycomb model in a quasi-1D geometry, we uncover its topological nature and show that it hosts Majorana zero modes localized at both ends, which are stabilized by finite-size-induced topology. We further show that the nonlocal Majorana fermion parity operator, $P_{\text{MF}}=i\gamma_{\text{L}}\gamma_{\text{R}}$, is mapped to a nonlocal spin-string operator, producing an end-to-end spin correlation proportional to the product of $P_{\text{MF}}$ and total fermion parity operators when local perturbations remove redundant ground-state degeneracies while preserving the Majorana and total fermion parities in the flux-free sector. Numerical calculations confirm a finite nonlocal spin correlation generated by these Majorana zero modes without any local magnetization. Our results establish a concrete signature of intrinsic Majorana nonlocality in quantum spin liquids.