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

Laser Physics

Entanglement and discord in spin glass

C.Y. Koh, L. C. Kwek, Shuai Wang, You Quan Chong

Published Jan 11, 2013• 8 citations
Publisher

Abstract

We study entanglement and discord in spin glass. By using the Edwards–Anderson XX model, we consider the Hamiltonian for three and four particles for nearest neighbor and next nearest neighbor interactions and to solve for the entanglement through concurrence. With a fixed mean and changing variances for the coupling J , the concurrence and discord are numerically plotted against the temperature. For J = 1, the critical temperature is found to be 2.106. The entanglement was found to increase beyond the critical temperature as the variance increases. The spin–spin correlation for three particles is plotted as a function of temperature T .

DOI
10.1088/1054-660x/23/2/025202

Related papers

Entanglement and quantum spin glass

C.Y. Koh

The paper reviews the entanglement behavior of a 2-qubit system in a quantum spin glass using the Heisenberg XX model and the interaction of the system with a spin glass bath environment. In the first part, we study the entanglement (concurrence) for a 3- and 4-qubit with nearest neighbor interaction. With a fixed mean and varying standard deviation for the J coupling, the concurrence is numerically plotted with temperature for the different configurations. A general formula for the concurrence is given for n qubits at low temperature. In the second part, we study the concurrence of a 2-qubit system coupled to a spin glass bath environment with n = 2 to ≥ 4 qubits. The bath sites are coupled with random J coupling and varying applied magnetic field. A general formula for concurrence is given for mean J = 0 and B = 0 for n bath sites. For small random J and magnetic field B, a steady state is obtained with an approximate concurrence of 0.5, showing that the entanglement is preserved.

International Journal of Modern Physics B•Jun 11, 2014•4 citations

Entanglement in quantum spin glass and its applications

C.Y. Koh

Well-known theories like Edwards-Anderson and Sherrington-Kirkpatrick models together with some important experimental results for spin glass are introduced in chapter 1. However, there is no single model, capable of explaining all the experimental results obtained from the spin glass materials. We use the theory of quantum entanglement (concurrence) to explore the quantum correlations of a spin glass. Quantum entanglement is a useful physical resource for quantum information and communication. In chapter 2, we discuss how information is encoded and measured. The applications of quantum information in algorithms are also mentioned. As quantum information science is built upon the foundation of quantum mechanics, two important aspects of this area: Einstein, Podolsky and Rosen (EPR) gedanken experiment and the Bell's inequality are introduced in chapter 3. In chapter 4, we discuss the idea of density operator, together with the use of trace and partial trace, to describe the state of the composite system. In chapter 5, a short introduction is made on the various entanglement measures. In chapter 6, the analytical calculations of the concurrence for a 3- and 4-qubit XX model are presented. The plots of concurrence with different means and standard deviations for the 3- and 4-qubit are also presented and analyzed. The concurrence of a 2-qubit system coupled to a spin glass bath of n = 2 to 4 qubits is studied in chapter 7. With an initial separable state, the 2-qubit system reached a steady state in concurrence through time evolution when it is coupled to a quantum spin glass environment. The result is general and the behavior of the concurrence is believed to be similar for n > 4. The quantum discord is used for analyzing the XX model and presented in chapter 8. In addition, the concurrence and discord for the next nearest neighbour interaction have been plotted for 3- and 4-qubit. In chapter 9, the concurrence of the probes that are attached to a spin glass is investigated by varying the external applied magnetic field and the J coupling. By using the quantum dots (qubits) as the probe, it is possible to distinguish a spin glass from a non-spin glass with the different signatures (drop and spike) in the concurrence between the probes. The derived entanglement witness for susceptibility and specific heat capacity are used to distinguish an entangled region from an unentangled region for two different spin glass alloys: LiHoxY1-xF4 and CuxMn in chapter 10. In chapter 11, the entanglement properties of the XXZ Heisenberg (with Dzyaloshinskii-Moriya interaction) and Ising transverse field spin glass models are examined with the use of concurrence for N qubits at one-dimensional level. The concurrence for both models are obtained by using the Kadanoff''s renormalization group (RG) approach. By following the RG fl ow, a first-order and second-order phase transitions are observed by varying the standard deviation of the renormalized couplings. This thesis ends with a conclusion in chapter 12 with suggestions for future research.

•Jan 1, 2014•0 citations

Entanglement in the Mixed-three-spin $XXX$ Heisenberg Model with the Next-nearest-neighbour Interaction

Hamid Arian Zad

In this paper, we investigate thermal pairwise quantum correlation for any pair of spins of a mixed-three-spin XXX Heisenberg system (with spins connected together with the nearest-neighbour (NN) and that of the next-nearest-neighbour (NNN) coupling constants J 1 and J 2 ) by means of concurrence and quantum discord, as functions of temperature T , magnetic field B and the coupling constants J 2 and J 1 .Some comparisons between these measures of entanglement are done for next-nearest-neighbour spins.We also express some magnetic properties and discuss the behaviour of the system in some special critical points.Some interesting and novel discussions are done to introduce some entanglement witnesses.

Acta Physica Polonica B•Jan 1, 2015•8 citations

Global quantum correlations in finite-size spin chains

Steve Campbell, L Mazzola, Gabriele De Chiara +4 more

We perform an extensive study of the properties of global quantum correlations in finite-size one-dimensional quantum spin models at finite temperature. By adopting a recently proposed measure for global quantum correlations (Rulli and Sarandy 2011 Phys. Rev. A 84 042109), called global discord , we show that critical points can be neatly detected even for many-body systems that are not in their ground state. We consider the transverse Ising model, the cluster-Ising model where three-body couplings compete with an Ising-like interaction, and the nearest-neighbor XX Hamiltonian in transverse magnetic field. These models embody our canonical examples showing the sensitivity of global quantum discord close to criticality. For the Ising model, we find a universal scaling of global discord with the critical exponents pertaining to the Ising universality class.

arXiv:1301.7114•New Journal of Physics•Apr 19, 2013•69 citations

Numerical studies of the compressible Ising spin glass

Adam H. Marshall, Bulbul Chakraborty, Sidney R. Nagel

We study a two-dimensional compressible Ising spin glass at constant volume. The spin interactions are coupled to the distance between neighboring particles in the Edwards-Anderson model with ± J interactions. We find that the energy of a given spin configuration is shifted from its incompressible value, E 0 , by an amount quadratic in E 0 and proportional to the coupling strength. We then construct a simple model expressed only in terms of spin variables that predicts the existence of a critical value of the coupling above which the spin-glass transition cannot exist.

arXiv:cond-mat/0509280•Europhysics Letters (EPL)•Apr 4, 2006•4 citations

Entanglement properties of XX model with three spin interactions

Xiu Zhang

Using the Concurrence criterion,we investigate the entanglement properties of XX model with three spin interactions.The effects of the three spin interaction J_2 and temperature T on the entanglement are discussed in both ferromagnetic and anti-ferromagnetic cases.Our results show that J_2 enhances the entanglement of the system,but the extent is difference for ferromagnetic and anti-ferromagnetic cases.J_2 also affects the critical temperature T_C,at which the entanglement disappears.T_C decreases with the increasing of J_2.Moreover,our results also indicate that the maximal entanglement increases with the decreasing of system temperature T.In addition,we also investigate the pairwise entanglement of the eigenstates of the Hamiltonian and discuss the ground-state entanglement.We obtain the quantum critical point at which the quantum phase transition takes place.

Journal of Atomic and Molecular Physics•Jan 1, 2010•0 citations
We study entanglement and discord in spin glass. By using the Edwards–Anderson XX model, we consider the Hamiltonian for three and four particles for nearest neighbor and next nearest neighbor interactions and to solve for the entanglement through concurrence. With a fixed mean and changing variances for the coupling J , the concurrence and discord are numerically plotted against the temperature. For J = 1, the critical temperature is found to be 2.106. The entanglement was found to increase beyond the critical temperature as the variance increases. The spin–spin correlation for three particles is plotted as a function of temperature T .
The paper reviews the entanglement behavior of a 2-qubit system in a quantum spin glass using the Heisenberg XX model and the interaction of the system with a spin glass bath environment. In the first part, we study the entanglement (concurrence) for a 3- and 4-qubit with nearest neighbor interaction. With a fixed mean and varying standard deviation for the J coupling, the concurrence is numerically plotted with temperature for the different configurations. A general formula for the concurrence is given for n qubits at low temperature. In the second part, we study the concurrence of a 2-qubit system coupled to a spin glass bath environment with n = 2 to ≥ 4 qubits. The bath sites are coupled with random J coupling and varying applied magnetic field. A general formula for concurrence is given for mean J = 0 and B = 0 for n bath sites. For small random J and magnetic field B, a steady state is obtained with an approximate concurrence of 0.5, showing that the entanglement is preserved.
Well-known theories like Edwards-Anderson and Sherrington-Kirkpatrick models together with some important experimental results for spin glass are introduced in chapter 1. However, there is no single model, capable of explaining all the experimental results obtained from the spin glass materials. We use the theory of quantum entanglement (concurrence) to explore the quantum correlations of a spin glass. Quantum entanglement is a useful physical resource for quantum information and communication. In chapter 2, we discuss how information is encoded and measured. The applications of quantum information in algorithms are also mentioned. As quantum information science is built upon the foundation of quantum mechanics, two important aspects of this area: Einstein, Podolsky and Rosen (EPR) gedanken experiment and the Bell's inequality are introduced in chapter 3. In chapter 4, we discuss the idea of density operator, together with the use of trace and partial trace, to describe the state of the composite system. In chapter 5, a short introduction is made on the various entanglement measures. In chapter 6, the analytical calculations of the concurrence for a 3- and 4-qubit XX model are presented. The plots of concurrence with different means and standard deviations for the 3- and 4-qubit are also presented and analyzed. The concurrence of a 2-qubit system coupled to a spin glass bath of n = 2 to 4 qubits is studied in chapter 7. With an initial separable state, the 2-qubit system reached a steady state in concurrence through time evolution when it is coupled to a quantum spin glass environment. The result is general and the behavior of the concurrence is believed to be similar for n > 4. The quantum discord is used for analyzing the XX model and presented in chapter 8. In addition, the concurrence and discord for the next nearest neighbour interaction have been plotted for 3- and 4-qubit. In chapter 9, the concurrence of the probes that are attached to a spin glass is investigated by varying the external applied magnetic field and the J coupling. By using the quantum dots (qubits) as the probe, it is possible to distinguish a spin glass from a non-spin glass with the different signatures (drop and spike) in the concurrence between the probes. The derived entanglement witness for susceptibility and specific heat capacity are used to distinguish an entangled region from an unentangled region for two different spin glass alloys: LiHoxY1-xF4 and CuxMn in chapter 10. In chapter 11, the entanglement properties of the XXZ Heisenberg (with Dzyaloshinskii-Moriya interaction) and Ising transverse field spin glass models are examined with the use of concurrence for N qubits at one-dimensional level. The concurrence for both models are obtained by using the Kadanoff''s renormalization group (RG) approach. By following the RG fl ow, a first-order and second-order phase transitions are observed by varying the standard deviation of the renormalized couplings. This thesis ends with a conclusion in chapter 12 with suggestions for future research.
Entanglement in the Mixed-three-spin XXXXXXXXX Heisenberg Model with the Next-nearest-neighbour Interaction
In this paper, we investigate thermal pairwise quantum correlation for any pair of spins of a mixed-three-spin XXX Heisenberg system (with spins connected together with the nearest-neighbour (NN) and that of the next-nearest-neighbour (NNN) coupling constants J 1 and J 2 ) by means of concurrence and quantum discord, as functions of temperature T , magnetic field B and the coupling constants J 2 and J 1 .Some comparisons between these measures of entanglement are done for next-nearest-neighbour spins.We also express some magnetic properties and discuss the behaviour of the system in some special critical points.Some interesting and novel discussions are done to introduce some entanglement witnesses.
We perform an extensive study of the properties of global quantum correlations in finite-size one-dimensional quantum spin models at finite temperature. By adopting a recently proposed measure for global quantum correlations (Rulli and Sarandy 2011 Phys. Rev. A 84 042109), called global discord , we show that critical points can be neatly detected even for many-body systems that are not in their ground state. We consider the transverse Ising model, the cluster-Ising model where three-body couplings compete with an Ising-like interaction, and the nearest-neighbor XX Hamiltonian in transverse magnetic field. These models embody our canonical examples showing the sensitivity of global quantum discord close to criticality. For the Ising model, we find a universal scaling of global discord with the critical exponents pertaining to the Ising universality class.
We study a two-dimensional compressible Ising spin glass at constant volume. The spin interactions are coupled to the distance between neighboring particles in the Edwards-Anderson model with ± J interactions. We find that the energy of a given spin configuration is shifted from its incompressible value, E 0 , by an amount quadratic in E 0 and proportional to the coupling strength. We then construct a simple model expressed only in terms of spin variables that predicts the existence of a critical value of the coupling above which the spin-glass transition cannot exist.
Using the Concurrence criterion,we investigate the entanglement properties of XX model with three spin interactions.The effects of the three spin interaction J_2 and temperature T on the entanglement are discussed in both ferromagnetic and anti-ferromagnetic cases.Our results show that J_2 enhances the entanglement of the system,but the extent is difference for ferromagnetic and anti-ferromagnetic cases.J_2 also affects the critical temperature T_C,at which the entanglement disappears.T_C decreases with the increasing of J_2.Moreover,our results also indicate that the maximal entanglement increases with the decreasing of system temperature T.In addition,we also investigate the pairwise entanglement of the eigenstates of the Hamiltonian and discuss the ground-state entanglement.We obtain the quantum critical point at which the quantum phase transition takes place.