Multipartite quantum nonlocality and topological quantum phase transitions in a spin-1/2 two-leg Kitaev ladder

Multipartite nonlocality, a measure of multipartite quantum correlations, is used to characterize topological quantum phase transitions (QPTs) in an infinite-size spin-1/2 two-leg Kitaev ladder model. First of all, the nonlocality measure $${\mathcal {S}}$$ is singular at the critical points, thus these topological QPTs are accompanied by dramatic changes of multipartite quantum correlations. The influence of the inter-chain coupling upon multipartite nonlocality is also investigated. Furthermore, we carry out scaling analysis and find that the logarithm measure scales linearly as $$\log _2{\mathcal {S}}_n \sim {\mathcal {K}} n +b$$ , with n the length of the concerned subchain. It is clear that the slope $${\mathcal {K}}$$ plays a central role in the large-n behavior of the nonlocality in the ladder. Especially, as n increases, we find the finite-size slope $${\mathcal {K}}_n$$ converges slowly in the $$\varDelta _{x,y}$$ phases which present non-local string orders, and quite rapidly in the $$\varDelta _0$$ phase which does not present any string order. We figure out a clear picture to explain these different behaviors.