Propagation of the interaction generating the macroscopic entanglement in a XX spin- $$\frac{1} {2}$$ chain with a staggered magnetic field

Abstract

An effective Poynting vector associated to a XX chain of a spin-\(\frac{1} {2}\) with staggered magnetic field, B l = B + e −iπl b is derived. Such a field is not likely to occur in nature although the model is analytically solvable and allows to study macroscopic correlation (entanglement witnessing) [J. Hide, W. Son, I. Lawrie, V. Vedral, Phys. Rev. A 76, 022319 (2007)]. It is found that the propagation of the interaction generating of the macroscopic correlations has a component which is not along to the axis of the chain. This questions the idea that the propagation of the macroscopic (multipartite) entanglement takes place exclusively along the axis of the chain of XX spin-\(\frac{1} {2}\). We point out that in general, that the propagation of macroscopic entanglement is not an one-dimensional phenomenon but this occurs in a region of the space. Some reliable criteria for macroscopic correlation in terms of our effective Poynting’s vector are derived. Associated with entanglement propagation, an effective group velocity by volume unit that satisfies a Lieb-Robinson-like upper bound for the velocity of the propagation of the information has been found.