Entanglement study of the 1D Ising model with Added Dzyaloshinsky-Moriya interaction

TL;DR

This study investigates quantum phase transitions in a 1D Ising model with Dzyaloshinsky-Moriya interaction using entanglement measures, revealing critical points and entanglement behavior with novel estimators and numerical methods.

Contribution

It introduces a new entanglement ratio as an estimator for quantum phase transitions and applies matrix product states to analyze entanglement in the presence of DM interaction.

Findings

Entanglement ratio minimum indicates the critical point.

Global and multipartite entanglement peak at the phase transition.

Matrix product state calculations confirm numerical results.

Abstract

We have studied occurrence of quantum phase transition in the one-dimensional spin-1/2 Ising model with added Dzyaloshinsky-Moriya (DM) interaction from bi- partite and multi-partite entanglement point of view. Using exact numerical solutions, we are able to study such systems up to 24 qubits. The minimum of the entanglement ratio R $\equiv$ \tau 2/\tau 1 < 1, as a novel estimator of QPT, has been used to detect QPT and our calculations have shown that its minimum took place at the critical point. We have also shown both the global-entanglement (GE) and multipartite entanglement (ME) are maximal at the critical point for the Ising chain with added DM interaction. Using matrix product state approach, we have calculated the tangle and concurrence of the model and it is able to capture and confirm our numerical experiment result. Lack of inversion symmetry in the presence of DM interaction stimulated us to study entanglement of three qubits in symmetric and antisymmetric way which brings some surprising results.