Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Physics Letters

Renormalization of Tripartite Entanglement in Spin Systems with Dzyaloshinskii–Moriya Interaction

Meng Qin, Li Wang, Bili Wang, Xiao Wang, Zhong Bai, Yanbiao Li

Published Oct 1, 2018• 3 citations
Publisher

Abstract

Quantum entanglement represents a fundamental feature of quantum many-body systems. We combine tripartite entanglement with quantum renormalization group theory to study the quantum critical phenomena. The Ising model and the Heisenberg X X Z model in the presence of the Dzyaloshinskii–Moriya interaction are adopted as the research objects. We identify that the tripartite entanglement can signal the critical point. The derivative of tripartite entanglement shows singularity as the spin chain size increases. Furthermore, the intuitive scaling behavior of the system selected is studied and the result allows us to precisely quantify the correlation exponent by utilizing the power law .

DOI
10.1088/0256-307x/35/10/100301

Related papers

Quantum coherence of an XY spin chain with Dzyaloshinskii-Moriya interaction and quantum phase transition

Guo-Qing Zhang, Jing‐Bo Xu

Abstract We investigate the quantum coherence of an XY spin chain with Dzyaloshinskii–Moriya interaction using a quantum renormalization group-based method, and show that the relative entropy of coherence increases with Dzyaloshinskii–Moriya interaction strength at zero temperature, as well as at finite temperature. We also study the quantum criticality of the system by making use of the relative entropy of coherence and violation of Bell inequality, and find that the first derivatives of the renormalized quantum coherence exhibit singularity near the critical point of the quantum phase transition. Finally, we explore the finite-size scaling behaviors of the derivatives of the quantum coherence at the critical point of the quantum phase transition, and obtain several universal finite-size scaling laws.

Journal of Physics A Mathematical and Theoretical•Jun 8, 2017•9 citations

Phase diagram and entanglement of the Ising model with Dzyaloshinskii-Moriya interaction

Rouhollah Jafari, Mehdi Kargarian, A. Langari +1 more

We have studied the phase diagram and entanglement of the one-dimensional Ising model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization-group (QRG) approach to get the stable fixed points, critical point, and the scaling of coupling constants. This model has two phases: antiferromagnetic and saturated chiral ones. We have shown that the staggered magnetization is the order parameter of the system and DM interaction produces the chiral order in both phases. We have also implemented the exact diagonalization (Lanczos) method to calculate the static structure factors. The divergence of structure factor at the ordering momentum as the size of systems goes to infinity defines the critical point of the model. Moreover, we have analyzed the relevance of the entanglement in the model which allows us to shed insight on how the critical point is touched as the size of the system becomes large. Nonanalytic behavior of entanglement and finite-size scaling have been analyzed which is tightly connected to the critical properties of the model. It is also suggested that a spin-fluid phase has a chiral order in terms of spin operators which are defined by a nonlocal transformation.

arXiv:0804.4579•Physical Review B•Dec 10, 2008•162 citations

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

Wajid Joyia, Khalid Khan

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.

International Journal of Quantum Information•Apr 1, 2017•2 citations

Quantum entanglement and quantum phase transition in the XY model with staggered Dzyaloshinskii-Moriya interaction

Fu-Wu Ma, Shengxin Liu, Xiang-Mu Kong

We study the quantum entanglement and quantum phase transition (QPT) of the anisotropic spin-$1/2$ $XY$ model with staggered Dzyaloshinskii-Moriya (DM) interaction by means of the quantum renormalization group method. The scaling of coupling constants and the critical points of the system are obtained. It is found that when the number of renormalization group iterations tends to infinity, the system exhibit a QPT between the spin-fluid and N\'eel phases which correspond with two saturated values of the concurrence for a given value of the strength of DM interaction. The DM interaction can enhance the entanglement and influence the QPT of the system. To gain further insight, the first derivative of the entanglement exhibit a nonanalytic behavior at the critical point and it directly associates with the divergence of the correlation length. This shows that the correlation length exponent is closely related to the critical exponent, i.e., the scaling behaviors of the system.

arXiv:1106.0901•Physical Review A•Oct 3, 2011•87 citations

Dynamical dephasing of bipartite and tripartite quantum coherence of spin-1/2 XXZ Heisenberg model in a renormalization group approach

Georges Collince Fouokeng, I Nsangou, F. Kuate Fodouop +2 more

Abstract The dynamical dephasing of a bipartite and tripartite quantum coherence in spin-1/2 Heisenberg model, driven by an applied magnetic field, in the presence of Dzyaloshinskii-Moriya interaction is investigated. The system is renormalized through the Kadanoof’s blocks approach. It is observed for both bipartite and tripartite schemes that by increasing the size of the system, the quantum coherence measure show an abrupt change at a quantum critical point (QCP). A further increase of the Dzyaloshinskii-Moriya coupling parameter affect the QCP, causing the dynamical dephasing which is the signature of second order quantum phase transition. The displacement of the QCP reduces the Quantum coherence of the system and can be controlled by the external magnetic field strength. Moreover, in a given range of Dzyaloshinskii-Moriya interaction strength and magnetic field, the monogamous and polygamous nature of quantum coherence is related to the size of the system.

Journal of Physics Communications•Apr 28, 2022•1 citation

Quantum Renormalization of Spin Squeezing in Spin Chains

Leila Balazadeh, G. Najarbashi, Ali Tavana

By employing quantum renormalization group (QRG) method, we investigate quantum phase transitions (QPT) in the Ising transverse field (ITF) model and in the XXZ Heisenberg model, with and without Dzyaloshinskii Moriya (DM) interaction, on a periodic chain of N lattice sites. We adopt a new approach called spin squeezing as an indicator of QPT. Spin squeezing, through analytical expression of a spin squeezing parameter, is calculated after each step of QRG. As the scale of the system becomes larger, (after many QRG steps), the ground state (GS) spin squeezing parameters show an abrupt change at a quantum critical point (QCP). Moreover, in all of the studied models, the first derivative of the spin squeezing parameter with respect to the control parameter is discontinuous, which is a signature of QPT. The spin squeezing parameters develop their saturated values after enough QRG iterations. The divergence exponent of the first derivative of the spin squeezing parameter in the near vicinity of the QCP is associated with the critical exponent of the correlation length.

Scientific Reports•Dec 6, 2018•10 citations
Quantum entanglement represents a fundamental feature of quantum many-body systems. We combine tripartite entanglement with quantum renormalization group theory to study the quantum critical phenomena. The Ising model and the Heisenberg X X Z model in the presence of the Dzyaloshinskii–Moriya interaction are adopted as the research objects. We identify that the tripartite entanglement can signal the critical point. The derivative of tripartite entanglement shows singularity as the spin chain size increases. Furthermore, the intuitive scaling behavior of the system selected is studied and the result allows us to precisely quantify the correlation exponent by utilizing the power law .
Abstract We investigate the quantum coherence of an XY spin chain with Dzyaloshinskii–Moriya interaction using a quantum renormalization group-based method, and show that the relative entropy of coherence increases with Dzyaloshinskii–Moriya interaction strength at zero temperature, as well as at finite temperature. We also study the quantum criticality of the system by making use of the relative entropy of coherence and violation of Bell inequality, and find that the first derivatives of the renormalized quantum coherence exhibit singularity near the critical point of the quantum phase transition. Finally, we explore the finite-size scaling behaviors of the derivatives of the quantum coherence at the critical point of the quantum phase transition, and obtain several universal finite-size scaling laws.
We have studied the phase diagram and entanglement of the one-dimensional Ising model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization-group (QRG) approach to get the stable fixed points, critical point, and the scaling of coupling constants. This model has two phases: antiferromagnetic and saturated chiral ones. We have shown that the staggered magnetization is the order parameter of the system and DM interaction produces the chiral order in both phases. We have also implemented the exact diagonalization (Lanczos) method to calculate the static structure factors. The divergence of structure factor at the ordering momentum as the size of systems goes to infinity defines the critical point of the model. Moreover, we have analyzed the relevance of the entanglement in the model which allows us to shed insight on how the critical point is touched as the size of the system becomes large. Nonanalytic behavior of entanglement and finite-size scaling have been analyzed which is tightly connected to the critical properties of the model. It is also suggested that a spin-fluid phase has a chiral order in terms of spin operators which are defined by a nonlocal transformation.
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.
We study the quantum entanglement and quantum phase transition (QPT) of the anisotropic spin-1/21/21/2 XYXYXY model with staggered Dzyaloshinskii-Moriya (DM) interaction by means of the quantum renormalization group method. The scaling of coupling constants and the critical points of the system are obtained. It is found that when the number of renormalization group iterations tends to infinity, the system exhibit a QPT between the spin-fluid and N\'eel phases which correspond with two saturated values of the concurrence for a given value of the strength of DM interaction. The DM interaction can enhance the entanglement and influence the QPT of the system. To gain further insight, the first derivative of the entanglement exhibit a nonanalytic behavior at the critical point and it directly associates with the divergence of the correlation length. This shows that the correlation length exponent is closely related to the critical exponent, i.e., the scaling behaviors of the system.
Abstract The dynamical dephasing of a bipartite and tripartite quantum coherence in spin-1/2 Heisenberg model, driven by an applied magnetic field, in the presence of Dzyaloshinskii-Moriya interaction is investigated. The system is renormalized through the Kadanoof’s blocks approach. It is observed for both bipartite and tripartite schemes that by increasing the size of the system, the quantum coherence measure show an abrupt change at a quantum critical point (QCP). A further increase of the Dzyaloshinskii-Moriya coupling parameter affect the QCP, causing the dynamical dephasing which is the signature of second order quantum phase transition. The displacement of the QCP reduces the Quantum coherence of the system and can be controlled by the external magnetic field strength. Moreover, in a given range of Dzyaloshinskii-Moriya interaction strength and magnetic field, the monogamous and polygamous nature of quantum coherence is related to the size of the system.
By employing quantum renormalization group (QRG) method, we investigate quantum phase transitions (QPT) in the Ising transverse field (ITF) model and in the XXZ Heisenberg model, with and without Dzyaloshinskii Moriya (DM) interaction, on a periodic chain of N lattice sites. We adopt a new approach called spin squeezing as an indicator of QPT. Spin squeezing, through analytical expression of a spin squeezing parameter, is calculated after each step of QRG. As the scale of the system becomes larger, (after many QRG steps), the ground state (GS) spin squeezing parameters show an abrupt change at a quantum critical point (QCP). Moreover, in all of the studied models, the first derivative of the spin squeezing parameter with respect to the control parameter is discontinuous, which is a signature of QPT. The spin squeezing parameters develop their saturated values after enough QRG iterations. The divergence exponent of the first derivative of the spin squeezing parameter in the near vicinity of the QCP is associated with the critical exponent of the correlation length.