Divergence of the entanglement range in low dimensional quantum systems

TL;DR

This paper investigates how pairwise entanglement behaves near separable ground states in one-dimensional quantum spin models, revealing a divergence in entanglement range and the transition from pairwise to multipartite entanglement at finite temperatures.

Contribution

It demonstrates the divergence of entanglement range near separable states and extends the analysis to quantum phase transitions in bosonic and fermionic systems.

Findings

Entanglement range diverges near separable ground states.

Different types of entanglement (parallel and antiparallel) are characterized.

Finite temperature leads to regions with only multipartite entanglement.

Abstract

We study the pairwise entanglement close to separable ground states of a class of one dimensional quantum spin models. At T=0 we find that such ground states separate regions, in the space of the Hamiltonian parameters, which are characterized by qualitatively different types of entanglement, namely parallel and antiparallel entanglement; we further demonstrate that the range of the Concurrence diverges while approaching separable ground states, therefore evidencing that such states, with uncorrelated fluctuations, are reached by a long range reshuffling of the entanglement. We generalize our results to the analysis of quantum phase transitions occurring in bosonic and fermionic systems. Finally, the effects of finite temperature are considered: At T>0 we evidence the existence of a region where no pairwise entanglement survives, so that entanglement, if present, is genuinely multipartite.