Three-Qubit Ground State and Thermal Entanglement of $XXZ$ Model With Dzyaloshinskii-Moriya Interaction

TL;DR

This paper investigates how Dzyaloshinskii-Moriya interaction and magnetic fields influence ground state and thermal entanglement in a three-qubit XXZ model, revealing conditions for entanglement enhancement and signatures of quantum phase transitions.

Contribution

It provides a detailed analysis of symmetric and non-symmetric pairwise entanglement in the presence of DM interaction and magnetic fields, highlighting new behaviors and critical phenomena.

Findings

Non-symmetric pairwise entanglement exceeds symmetric pairwise in concurrence and critical temperature.

Entanglement varies monotonically or non-monotonically with DM interaction depending on anisotropy.

Zero-temperature ground state entanglement indicates quantum phase transition signatures.

Abstract

We have studied the symmetric and non-symmetric pairwise ground state and thermal entanglement in three-qubit anisotropic Heisenberg (XXZ) and Ising in a magnetic field models and in the presence of Dzyaloshinskii-Moriya (DM) interaction. We have found that increasing of the DM interaction and magnetic field can enhance and reduce the entanglement of system. We have shown that the non-symmetric pairwise has higher value concurrence and critical temperature (above which the entanglement vanishes) than the symmetric pairwise. For negative anisotropy the non-symmetric entanglement is a monotonic function of DM interaction while for positive anisotropy it has a maximum versus DM parameter and vanishes for larger values of DM interaction. The conditions for the existence of thermal entanglement are discussed in details. The most remarkable result happens at zero temperature where 3-qubit ground state entanglement of the system (in spite of 2-qubit counterpart) shows the fingerprint of quantum phase transition for an infinite size system.