Distribution of entanglement with variable range interactions

TL;DR

This paper explores how variable range interactions in an anisotropic quantum XY model influence entanglement distribution, revealing conditions for entanglement growth, robustness against temperature, and the importance of factorization points.

Contribution

It introduces a detailed analysis of entanglement behavior in long-range interacting systems, highlighting the role of factorization points and interaction laws in entanglement robustness and distribution.

Findings

Entanglement between distant sites can grow with increasing interaction range.

Entanglement robustness against temperature is enhanced with longer-range interactions.

Shareability of bipartite entanglements is constrained by monogamy relations.

Abstract

Distribution of quantum entanglement is investigated for an anisotropic quantum XY model with variable range interactions and in the presence of a uniform transverse magnetic field. We report the possibility of \emph{qualitative} growth in the entanglement between distant sites with an increase in the range of interactions that vary either exponentially or polynomially as the distance between the sites increases. Interestingly, we find that such entanglement enhancement is not ubiquitous and is dependent on the factorization points, a specific set of system parameters where the zero-temperature state of the system is fully separable. In particular, we observe that at zero-temperature, when the system parameters are chosen beyond the pair of factorization points, the increments in entanglement length due to variable range interactions are more pronounced compared to the situation when the parameters lie in between the factorization points. By employing the sum of all the bipartite entanglements with respect to a single site, we also show that the shareability of the bipartite entanglements are constrained, thereby establishing their monogamous nature. Furthermore, we note that the factorization points get reallocated depending on the laws of interaction fall-offs and provide an ansatz for the same. We reveal that the temperature at which the canonical equilibrium state becomes entangled from an unentangled one increases with the increase in the range of interactions, thereby demonstrating enhanced robustness in entanglement against temperature in the presence of long-range interactions and only when the system parameters are chosen between the pair of factorization points. We apply an energy-based entanglement witness to provide a justification to the observed robustness with temperature.