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

Journal of the Physical Society of Japan

Quantum Coherence and Skew Information with Quantum Phase Transition in One-Dimensional Anisotropic XY Model under Renormalization Group Method

Muhammad Javed, Muhammad Musadiq, Mahmood Shamirzaie, Salman Khan

Published Oct 1, 2021• 2 citations
Publisher

Abstract

We investigate the behaviors of Wigner–Yanase skew information and the l1 norm, as two different measures of quantum coherence, in a tripartite ground state of the anisotropic spin-1/2 XY model. Following the renormalization-group method, we analytically link the two measures with each other and with the ground state energy of the system. We demonstrate that both the quantities show distinctive behaviors at the critical point of the system. The analysis of the first derivatives of the quantities reveals nonanalyticity in their behaviors, capturing quantum phase transition. The scaling behavior of the system is analyzed and it is shown that the minimum of the first derivative of Wigner–Yanase skew information converges to zero and the maximum of the first derivative of l1 norm diverges and both approach to the critical point with increasing size of the system.

DOI
10.7566/jpsj.90.104005

Related papers

Entanglement and quantum phase transition in the one-dimensional anisotropic XY model

Fu-Wu Ma, Sheng-Xin Liu, Xiang-Mu Kong

In this paper the entanglement and quantum phase transition of the anisotropic spin-$1/2$ $\mathit{XY}$ model are studied by using the quantum renormalization-group method. By solving the renormalization equations, we get the trivial and nontrivial fixed points, which correspond to the phase of the system and the critical point, respectively. The concurrence between two blocks are calculated and it is found that when the number of iterations of the renormalization tends to infinity, the concurrence develops two saturated values that are associated with two different phases, i.e., Ising-like and spin-fluid phases. We also investigate the first derivative of the concurrence and find that there exists nonanalytic behaviors at the quantum critical point, which are directly associated with the divergence of the correlation length. To gain further insight, the scaling behaviors of the system are analyzed and it is shown that the maximum value of the first derivative of the concurrence reaches infinity and the critical point is approached as the size of the system increases.

arXiv:1105.1671•Physical Review A•Jun 7, 2011•86 citations

Quantum coherence and uncertainty in the anisotropic XY chain

Göktuğ Karpat, Barış Çakmak, F. F. Fanchini

We explore the local quantum coherence and the local quantum uncertainty, based on Wigner-Yanase skew information, in the ground state of the anisotropic spin-1/2 XY chain in a transverse magnetic field. We show that the skew information, as a figure of merit, supplies the necessary information to reveal the occurrence of the second-order phase transition and the completely factorized ground state in the XY model. Additionally, in the same context, we also discuss the usefulness of a simple experimentally friendly lower bound of local quantum coherence. Furthermore, we demonstrate how the connection between the appearance of nonanalyticities in the local quantum uncertainty of the ground state and the quantum phase transitions does not hold in general, by providing explicit examples of the situation. Lastly, we discuss the ability of the local quantum coherence to accurately estimate the critical point of the phase transition, and we investigate the robustness of the factorization phenomenon at low temperatures.

arXiv:1404.6427•Physical Review B•Sep 30, 2014•234 citations

Signature of topological quantum phase transitions via Wigner-Yanase skew information

W. W. Cheng, Z. Z. Du, Longyan Gong +2 more

\n\nWe apply the Wigner-Yanase skew information approach to analyze two typical models that exhibit a topological quantum phase transition. Based on the exact solutions of the ground states, the Wigner-Yanase skew information between two nearest sites for each of the two models is obtained. For the one-dimensional Kitaev chain model, the first-order derivative of the Wigner-Yanase skew information is non-analytical around the critical point. The scaling behavior and the universality are verified numerically. In particular, the skew information can also detect the factorization transition in such a model. For the two-dimensional Kitaev honeycomb model, the first-order derivative of the Wigner-Yanase skew information shows some singularities at the critical points where the system transits from the gapless phase to the gapped one. Our results suggest that the Wigner-Yanase skew information can serve as a good indicator of the topological phase transitions in these models and shed considerable light on the relationships between topological quantum phase transition and information theory.\n

Europhysics Letters (EPL)•Nov 1, 2014•25 citations

Spin nonclassicality and quantum phase transition in the XY spin model

Hao Dai, Shuangshuang Fu, Shunlong Luo

Abstract We study the behaviors of spin nonclassicality in critical systems of spin chains, with the spin nonclassicality measured by an informational quantifier based on the Wigner-Yanase skew information. For the XY spin chain with three-spin interaction, we evaluate both the single-spin and the nearest neighbour two-spin nonclassicalities, as well as their first-order derivatives. We demonstrate the effectiveness of these quantities of spin nonclassicality in revealing the critical points for quantum phase transition. The merits of the present approach to detecting quantum phase transition by spin nonclassicality lie in its easy computation, informational content and metrological significance.

Physica Scripta•Sep 16, 2020•5 citations

Investigation of the Behavior of Quantum Coherence in Quantum Phase Transitions of Two-Dimensional XY and Ising Models

Narjes Taghadomi, Azam Mani, Ali Bakouei

We investigate the behavior of quantum coherence of the ground states of 2D Heisenberg XY model and 2D Ising model with transverse field on square lattices, by using the method of Quantum Renormalization Group (QRG). We show that the non-analytic behavior of quantum coherence near the critical point, can detect quantum phase transition (QPT) of these models. We also use the scaling behavior of maximum derivative of quantum coherence, with system size, to find the critical exponent of coherence for both models and also the length exponent of the Ising model. The results are in close agreement with the ones obtained from entanglement analysis, that is while quantum coherence needs less computational calculations in comparison to entanglement approaches.

arXiv:2208.00158•Jul 30, 2022•0 citations

Dynamics of entanglement in the one-dimensional anisotropic XXZ model

Han Zhang, Yu-Liang Xu, Rong-Tao Zhang +4 more

The dynamics of entanglement in the one-dimensional spin-1/2 anisotropic XXZ model is studied using the quantum renormalization-group method. We obtain the analytical expression of the concurrence, for two different quenching methods, it is found that initial state plays a key role in the evolution of system entanglement, i.e., the system returns completely to the initial state every other period. Our computations and analysis indicate that the first derivative of the characteristic time at which the concurrence reaches its maximum or minimum with respect to the anisotropic parameter occurs nonanalytic behaviors at the quantum critical point. Interestingly, the minimum value of the first derivative of the characteristic time versus the size of the system exhibits the scaling behavior which is the same as the scaling behavior of the system ground-state entanglement in equilibrium. In particular, the scaling behavior near the critical point is independent of the initial state.

arXiv:2004.04008•Apr 8, 2020•0 citations
We investigate the behaviors of Wigner–Yanase skew information and the l1 norm, as two different measures of quantum coherence, in a tripartite ground state of the anisotropic spin-1/2 XY model. Following the renormalization-group method, we analytically link the two measures with each other and with the ground state energy of the system. We demonstrate that both the quantities show distinctive behaviors at the critical point of the system. The analysis of the first derivatives of the quantities reveals nonanalyticity in their behaviors, capturing quantum phase transition. The scaling behavior of the system is analyzed and it is shown that the minimum of the first derivative of Wigner–Yanase skew information converges to zero and the maximum of the first derivative of l1 norm diverges and both approach to the critical point with increasing size of the system.
In this paper the entanglement and quantum phase transition of the anisotropic spin-1/21/21/2 XY\mathit{XY}XY model are studied by using the quantum renormalization-group method. By solving the renormalization equations, we get the trivial and nontrivial fixed points, which correspond to the phase of the system and the critical point, respectively. The concurrence between two blocks are calculated and it is found that when the number of iterations of the renormalization tends to infinity, the concurrence develops two saturated values that are associated with two different phases, i.e., Ising-like and spin-fluid phases. We also investigate the first derivative of the concurrence and find that there exists nonanalytic behaviors at the quantum critical point, which are directly associated with the divergence of the correlation length. To gain further insight, the scaling behaviors of the system are analyzed and it is shown that the maximum value of the first derivative of the concurrence reaches infinity and the critical point is approached as the size of the system increases.
We explore the local quantum coherence and the local quantum uncertainty, based on Wigner-Yanase skew information, in the ground state of the anisotropic spin-1/2 XY chain in a transverse magnetic field. We show that the skew information, as a figure of merit, supplies the necessary information to reveal the occurrence of the second-order phase transition and the completely factorized ground state in the XY model. Additionally, in the same context, we also discuss the usefulness of a simple experimentally friendly lower bound of local quantum coherence. Furthermore, we demonstrate how the connection between the appearance of nonanalyticities in the local quantum uncertainty of the ground state and the quantum phase transitions does not hold in general, by providing explicit examples of the situation. Lastly, we discuss the ability of the local quantum coherence to accurately estimate the critical point of the phase transition, and we investigate the robustness of the factorization phenomenon at low temperatures.
\n\nWe apply the Wigner-Yanase skew information approach to analyze two typical models that exhibit a topological quantum phase transition. Based on the exact solutions of the ground states, the Wigner-Yanase skew information between two nearest sites for each of the two models is obtained. For the one-dimensional Kitaev chain model, the first-order derivative of the Wigner-Yanase skew information is non-analytical around the critical point. The scaling behavior and the universality are verified numerically. In particular, the skew information can also detect the factorization transition in such a model. For the two-dimensional Kitaev honeycomb model, the first-order derivative of the Wigner-Yanase skew information shows some singularities at the critical points where the system transits from the gapless phase to the gapped one. Our results suggest that the Wigner-Yanase skew information can serve as a good indicator of the topological phase transitions in these models and shed considerable light on the relationships between topological quantum phase transition and information theory.\n
Abstract We study the behaviors of spin nonclassicality in critical systems of spin chains, with the spin nonclassicality measured by an informational quantifier based on the Wigner-Yanase skew information. For the XY spin chain with three-spin interaction, we evaluate both the single-spin and the nearest neighbour two-spin nonclassicalities, as well as their first-order derivatives. We demonstrate the effectiveness of these quantities of spin nonclassicality in revealing the critical points for quantum phase transition. The merits of the present approach to detecting quantum phase transition by spin nonclassicality lie in its easy computation, informational content and metrological significance.
We investigate the behavior of quantum coherence of the ground states of 2D Heisenberg XY model and 2D Ising model with transverse field on square lattices, by using the method of Quantum Renormalization Group (QRG). We show that the non-analytic behavior of quantum coherence near the critical point, can detect quantum phase transition (QPT) of these models. We also use the scaling behavior of maximum derivative of quantum coherence, with system size, to find the critical exponent of coherence for both models and also the length exponent of the Ising model. The results are in close agreement with the ones obtained from entanglement analysis, that is while quantum coherence needs less computational calculations in comparison to entanglement approaches.
The dynamics of entanglement in the one-dimensional spin-1/2 anisotropic XXZ model is studied using the quantum renormalization-group method. We obtain the analytical expression of the concurrence, for two different quenching methods, it is found that initial state plays a key role in the evolution of system entanglement, i.e., the system returns completely to the initial state every other period. Our computations and analysis indicate that the first derivative of the characteristic time at which the concurrence reaches its maximum or minimum with respect to the anisotropic parameter occurs nonanalytic behaviors at the quantum critical point. Interestingly, the minimum value of the first derivative of the characteristic time versus the size of the system exhibits the scaling behavior which is the same as the scaling behavior of the system ground-state entanglement in equilibrium. In particular, the scaling behavior near the critical point is independent of the initial state.