Long-range multipartite quantum correlations and factorization in a one-dimensional spin-1/2 $XY$ chain

TL;DR

This paper investigates long-range multipartite quantum correlations in a one-dimensional spin-1/2 XY chain, revealing their role in quantum phase transitions, factorization points, and bound entanglement detection.

Contribution

It introduces new MQC measures based on entanglement negativity and formation, demonstrating their effectiveness in detecting phase transitions and ground state factorization.

Findings

Long-range MQCs exist even in the Ising case.

MQCs can detect quantum phase transitions and finite-size scaling.

MQCs can precisely indicate the ground state factorization point.

Abstract

We study the properties of multipartite quantum correlation (MQC) in a one-dimensional spin-1/2 $XY$ chain, where the three-spin reduced states are focused on and the four introduced MQC measures are based on entanglement negativity and entanglement of formation. It is found that, even in the Ising case, the three-spin subsystems have the long-range MQCs and the tripartite quantum correlations beyond the nearest-neighbor three spins can detect the quantum phase transition and obey the finite-size scaling around the critical point. Furthermore, in the $XY$ model, we show that the two selected MQCs can indicate exactly the factorization point of the ground state for the anisotropic model in the thermodynamic and finite-size cases. Moreover, the spatial distribution of MQC based on entanglement negativity can attain to a much larger range by tuning the anisotropic parameter, and the newly defined MQC based on entanglement of formation can detect the bound entanglement in the three-spin subsystems when the entanglement negativity loses its efficacy.