Mimicking quantum correlation of a long-range Hamiltonian by finite-range interactions

TL;DR

This paper demonstrates that the entanglement patterns of a quantum long-range Ising model can be effectively mimicked by a finite-range interaction model under moderate interaction strengths, revealing insights into entanglement distribution and monogamy.

Contribution

It shows that finite-range models can replicate the entanglement features of long-range quantum systems for moderate interactions, providing a new perspective on modeling quantum correlations.

Findings

Entanglement patterns are mimicked by finite-range models at moderate interactions.

Strong interactions lead to divergence in entanglement distribution from finite-range models.

Monogamy score aligns with pairwise entanglement behavior, saturating or decaying accordingly.

Abstract

The quantum long-range extended Ising model possesses several striking features that cannot be observed in the corresponding short-range model. We report that the pattern obtained from the entanglement between any two arbitrary sites of the long-range model can be mimicked by the model having a finite range of interactions provided the interaction strength is moderate. On the other hand, we illustrate that when the interactions are strong, the entanglement distribution in the long-range model does not match the class of a model with a few interactions. We also show that the monogamy score of entanglement is in good agreement with the behavior of pairwise entanglement. Specifically, it saturates when the entanglement in the finite-range Hamiltonian behaves similarly to the long-range model, while it decays algebraically otherwise.