Dzyaloshinskii–Moriya interaction and anisotropy effects on the tripartite quantum discord of Heisenberg XY model

2017 ◽  
Vol 15 (03) ◽  
pp. 1750021 ◽  
Author(s):  
Wajid Joyia ◽  
Khalid Khan
Keyword(s):  
Phase Transition ◽  
Renormalization Group ◽  
Critical Point ◽  
Quantum Phase Transition ◽  
Quantum Discord ◽  
Xy Model ◽  
Dm Interaction ◽  
Xy Chain ◽  
Moriya Interaction ◽  
Spin Fluid

In this paper, we address the tripartite quantum discord for the Heisenberg XY chain with the Dzyaloshinskii–Moriya (DM) interaction using the quantum renormalization-group (QRG) method. In thermodynamic limit, like the entanglement, the tripartite discord exhibits the quantum phase transition (QPT) between the spin-fluid and the Neel phases. The effect of the DM interaction and the anisotropy on the features of the tripartite quantum discord has been probed. It is noted that the DM interaction brings the critical point earlier and affects heavily with the size of the system. Moreover, the system requires a larger number of the iterations to achieve the QPT for the tripartite quantum discord as compared to the entanglement.

NEGATIVITY AND GEOMETRIC QUANTUM DISCORD AS INDICATORS OF QUANTUM PHASE TRANSITION IN THE XY MODEL WITH DZYALOSHINSKII–MORIYA INTERACTION

2013 ◽  
Vol 27 (16) ◽  
pp. 1350074 ◽  
Author(s):  
SHUAI XU ◽  
XUE KE SONG ◽  
LIU YE
Keyword(s):  
Phase Transition ◽  
Quantum Phase Transition ◽  
Quantum Discord ◽  
Anisotropy Parameter ◽  
Quantum Phase ◽  
Group Method ◽  
Xy Model ◽  
Anisotropic Parameter ◽  
Dm Interaction ◽  
Geometric Quantum Discord

In this paper, we use the negativity and geometric quantum discord (GQD) to investigate the quantum phase transition (QPT) in the anisotropic spin-1/2 XY model with staggered Dzyaloshinskii–Moriya (DM) interaction using the quantum renormalization-group method, and the results show that the negativity and GQD can both obtain the quantum critical points associated with QPTs after several iterations of the renormalization. In addition to this, we discuss how the strength of the DM interaction and anisotropic parameter make the effect on the negativity and GQD for different RG steps. At last, we give out the relationship between negativity and GQD, and verify that with anisotropy parameter and the strength of DM interaction increased, the squared negativity and the normalization of GQD tend to equal in this model.

Quantum phase transition for the XY chain with Dzyaloshinsky–Moriya interaction

2018 ◽  
Vol 16 (06) ◽  
pp. 1850051 ◽  
Author(s):  
Biao-Liang Ye ◽  
Yan Luo ◽  
Shu-Yuan Jiang ◽  
Dan Zhang ◽  
Jian-Qin Xu ◽  
...  
Keyword(s):  
Phase Transition ◽  
Quantum Phase Transition ◽  
Quantum Coherence ◽  
Coupling Parameter ◽  
Spin Model ◽  
Quantum Phase ◽  
Spin Models ◽  
Two Measures ◽  
Xy Chain ◽  
Moriya Interaction

We study quantum phase transition of the [Formula: see text] spin model with Dzyaloshinsky–Moriya interaction, by using quantum correlation measures, i.e. quantum deficit and measurement-induced disturbance. It is shown that as the Dzyaloshinsky–Moriya coupling parameter [Formula: see text] increases, the behaviors of quantum phase transition can be suppressed. We also investigate quantum phase transition for the Ising and [Formula: see text] spin models at finite temperature. It is found that quantum phase transition characterized by measurement-induced disturbance is greater than or equal to that characterized by quantum deficit. Other interesting analytical results and numerical results on quantum phase transition for the proposed spin models are also presented by applying the two measures. Furthermore, we also compare quantum deficit and measurement-induced disturbance with quantum entanglement, quantum discord and quantum coherence.

Geometric phase and the influence of the Dzyaloshinski–Moriya interaction in the one-dimensional quantum compass model

2015 ◽  
Vol 29 (25) ◽  
pp. 1550146 ◽  
Author(s):  
J. M. Lü ◽  
X. P. Li ◽  
L. C. Wang
Keyword(s):  
Phase Transition ◽  
Quantum Phase Transition ◽  
Geometric Phase ◽  
Spin Systems ◽  
Quantum Phase ◽  
Dm Interaction ◽  
One Dimensional ◽  
The One ◽  
Moriya Interaction

Geometric phase and quantum phase transition (QPT) of the one-dimensional (1D) quantum compass model with the Dzyaloshinski–Moriya (DM) interaction are investigated, and the effect of the DM interaction to the properties of geometric phase and QPTs of the model are discussed in this paper. Our study is an extension of the relation between the geometric phase and QPTs in the 1D spin systems.

Quantum correlations in Heisenberg XY spin-1 and spin-1/2 model with Dzyaloshinskii–Moriya interactions

2015 ◽  
Vol 13 (05) ◽  
pp. 1550035 ◽  
Author(s):  
Wajid Hussain Joyia
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
Quantum Phase Transition ◽  
Quantum Correlation ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
Spin Systems ◽  
Quantum Phase ◽  
Xy Model ◽  
Higher Spin

We study the quantum correlations in a spin-1/2 (qubit) and spin-1 (qutrit) Heisenberg XY model separately, based on quantum discord (QD) and measurement-induced disturbance (MID) respectively. We find the evidence of the first- and second-order quantum phase transition (QPT) in both spin-1/2 and spin-1 systems. The effect of the temperature, magnetic field and Dzyaloshinskii–Moriya (DM) interactions on QPT and quantum correlation are also investigated. Finally, we observed that the QD and MID are not only vigorous for higher spin systems but also more robust than entanglement.

scholarly journals Global quantum discord and quantum phase transition in XY model

2015 ◽  
Vol 362 ◽  
pp. 805-813 ◽  
Author(s):  
Si-Yuan Liu ◽  
Yu-Ran Zhang ◽  
Wen-Li Yang ◽  
Heng Fan
Keyword(s):  
Phase Transition ◽  
Quantum Phase Transition ◽  
Quantum Discord ◽  
Quantum Phase ◽  
Xy Model ◽  
Global Quantum Discord

Quantum coherence and quantum phase transition in the XY model with staggered Dzyaloshinsky-Moriya interaction

2017 ◽  
Vol 510 ◽  
pp. 7-12 ◽  
Author(s):  
Ning-Ju Hui ◽  
Yang-Yang Xu ◽  
Jicheng Wang ◽  
Yixin Zhang ◽  
Zheng-Da Hu
Keyword(s):  
Phase Transition ◽  
Quantum Phase Transition ◽  
Quantum Coherence ◽  
Quantum Phase ◽  
Xy Model ◽  
Moriya Interaction
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