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Journal of Hefei University

Entanglement Dynamics in Ising Model

Zhuo‐Liang Cao

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

Ising model is the simplest Heisenberg model,research on the entanglement of this model will promote the development of solid quantum computer.Considering the phase decoherence of system,this paper investigates the entanglement dynamics of two qubits Ising chain with the DM interaction.It is found that the effects of phase decoherence and DM interaction on entanglement are dependent on the initial state of system.For some initial states,the entanglement of system is invariable.For some others,with the increase of time,the entanglement of system oscillates and decreases.In addition,increasing the DM interaction will decrease the entanglement and the oscillation period;increasing the phase decoherence rate will also decrease the entanglement,however,the oscillation period is unchanging.

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Ising model is the simplest Heisenberg model,research on the entanglement of this model will promote the development of solid quantum computer.Considering the phase decoherence of system,this paper investigates the entanglement dynamics of two qubits Ising chain with the DM interaction.It is found that the effects of phase decoherence and DM interaction on entanglement are dependent on the initial state of system.For some initial states,the entanglement of system is invariable.For some others,with the increase of time,the entanglement of system oscillates and decreases.In addition,increasing the DM interaction will decrease the entanglement and the oscillation period;increasing the phase decoherence rate will also decrease the entanglement,however,the oscillation period is unchanging.
With considering the intrinsic decoherence, the dynamic behaviors of quantum entanglement in a three-qubit XXZ Heisenberg system with Dzyaloshinskii-Moriya (DM) interaction and anisotropy for different initial states are investigated. The research result shows that the anisotropy parameter does not affect the system entanglement, however, the intrinsic decoherence has obvious inhibitory effect on entanglement. When the initial state of system is an entangled state, we can obtain the stable value of entanglement by adjusting DM interaction parameters appropriately. As the system initial state is a separation state, entanglement oscillates, and the amplitude of oscillation decays with time periodically, and there will appear the death phenomenon after each oscillation, and with time going on, its concurrence will be zero. When the initial state is entangled, by choosing the proper DM parameter, the three pairs of entanglements oscillate with time and eventually approach to a steady value. The increase of accelerates the decay of concurrence. When the initial state is separated, entanglement oscillates, and the amplitude of oscillation decays with time periodically, and there will appear the death phenomenon after each oscillation, with time going on, its concurrence will be zero. Therefore, the proper initial state and DM interaction parameters can control the concurrence effectively under the intrinsic decoherence, thereby obtaining the preferable entanglement resource.
An investigation of the entanglement and fidelity for two-qubit Ising model in an external uniform magnetic field showed that the entanglement degree oscillated with increasing phase decoherence in the initial stage and decreased with the increase in phase decoherence thereafter,the decline of the entanglement degree being greater with greater phase decoherence.When the initial state of the system was on its eigenstate,the concurrence was zero,or it did not change with the evolution of phase decoherence.The fidelity of the system exhibied an obvious periodic change and tended to remain at a constant value with the increase in phase decoherence.The entanglement degree and fidelity of the two-qubit Ising model could be enhanced or weakened through controlling magnetic field B.
This paper investigates the entanglement dynamics of the system, composed of two qubits A and B with Heisenberg XX spin interactation. There is a third controller qubit C, which only has Dzyaloshinskii–Moriya (DM) spin-orbit interaction with the qubit B. It is found that depending on the initial state of the controller qubit C and DM interaction, the entanglement of the system displays amplification and sudden birth effects. These effects indicate that one can control the entanglement of the system, which may be helpful for quantum information processing.
Because the key issue in quantum information and quantum computing is entanglement, the investigation of the effects of environment, as a source of quantum dissipation, and interaction between environment and system on entanglement and quantum phase transition is important. In this paper, we consider two-qubit system in the anisotropic Heisenberg XXZ model with the Dzyaloshinskii-moriya interaction, and accompanied quantum dissipation. Using Lindblad dynamics, the coupling effect and also temperature effect on concurrence, as a measure of entanglement of system, is obtained. The role of DM interaction parameters in the evolution of entanglement is investigated. Furthermore, using derivative of concurrence, the effects of dissipation and DM interaction parameter on quantum phase transition are obtained. It should be noted that spin-orbit interaction or DM parameter intensively influence the process of impressments of dissipation on entanglement measure and quantum phase transition. The current research is very important in the topics of nanometric systems.
Employing the I-concurrence (Ic) measure, entanglement dynamics of superposition of isospin fermionic coherent states (SFCS) in Heisenberg spin chains of Ising, XX, XXX and XXZ models in the presence of Dzyaloshinskii–Moriya (DM) interaction and magnetic field is studied. For the above-mentioned models, the entanglement dynamics of SFCSs is independent of magnetic field effect and the DM interaction effect introduces the quantum fluctuations in the entanglement dynamics of the system. It is shown that depending on the choice of the models in the absence of DM interaction, entanglement dynamics alter by applying and increasing the magnetic field to the first (second) part of the system. We showed that by increasing the spin of the fermionic coherent states (j) and, consequently, increasing their dimension d = 2j + 1, the entanglement dynamics of the SFCS states sharply increases and fluctuates at a higher level. Our results indicate no entanglement sudden death phenomenon under the examined conditions.
We study the relationship between quench dynamics of entanglement and quantum phase transition in the antiferromagnetic Ising model with the Dzyaloshinskii–Moriya (DM) interaction by using the quantum renormalization-group method and the definition of negativity. Two types of quench protocols (i) adding the DM interaction suddenly and (ii) rotating the spins around x axis are considered to drive the dynamics of the system, respectively. By comparing the behaviors of entanglement in both types of quench protocols, the effects of quench on dynamics of entanglement are studied. It is found that there is the same characteristic time at which the negativity firstly reaches its maximum although the system shows different dynamical behaviors. Especially, the characteristic time can accurately reflect the quantum phase transition from antiferromagnetic to saturated chiral phases in the system. In addition, the correlation length exponent can be obtained by exploring the nonanalytic and scaling behaviors of the derivative of the characteristic time.