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Communications in Theoretical Physics

Entanglement and Fidelity of a Spin Ladder with Dzyaloshinsky—Moriya Interaction

Ya Chen, Shiqun Zhu

Published Dec 1, 2011• 5 citations
Publisher

Abstract

The spin ladder with Dzyaloshinsky—Moriya interaction is investigated by using the quantum renormalization-group method. The entanglement and fidelity are periodic functions of the time and oscillate between zero and one. The oscillation period decreases with either the interaction in the spin ladder or the Dzyaloshinsky—Moriya interaction increasing. When the system relates to the environment, both entanglement and fidelity oscillate with a damping rate related to intrinsic decoherence rate, the interaction in the spin ladder, and the Dzyaloshinsky—Moriya interaction.

DOI
10.1088/0253-6102/56/6/07

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The spin ladder with Dzyaloshinsky—Moriya interaction is investigated by using the quantum renormalization-group method. The entanglement and fidelity are periodic functions of the time and oscillate between zero and one. The oscillation period decreases with either the interaction in the spin ladder or the Dzyaloshinsky—Moriya interaction increasing. When the system relates to the environment, both entanglement and fidelity oscillate with a damping rate related to intrinsic decoherence rate, the interaction in the spin ladder, and the Dzyaloshinsky—Moriya interaction.
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We study the time evolution of decoherence factor of two spin qubits and qutrits coupled to an XYXYXY spin chain with Dzyaloshinsky-Moriya (DM) interaction environment. The dynamical process of the decoherence is numerically and analytically investigated. We find that the DM interaction can enhance slightly the decay of the decoherence factor in the weak-coupling region. However, in the strong-coupling region, the decoherence factor is very sensitive to the DM interaction.
Using the Milburn equation, we have studied the properties of the entanglement and fidelity dynamics in a spin system with different Dzyaloshinskii-Moriya interaction and magnetic field in detail. Effects of different Dzyaloshinskii-Moriya interaction, different magnetic fields, and the initial states on the entanglement and fidelity are discussed. Results show that entanglement decoherence can be suppressed by inhomogeneous magnetic fields. Initial state affects greatly the entanglement, and a proper entanglement can be obtained by adjusting the directions of Dzyaloshinskii-Moriya interaction. For a particular initial state, an optimal fidelity is obtained by changing the direction of the Dzyaloshinskii-Moriya interaction. Moreover, no matter how homogeneous or inhomogeneous the magnetic fields are, they cannot enhance the fidelity. The dependence of entanglement and fidelity on the angle of initial state shows periodicity. Hence we can select an optimal initial state for a specific condition according to requirement.
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.
We study the effects of the Dzyaloshinski-Moriya (DM) anisotropic interaction on the ground-state properties of the Heisenberg XY spin chain by means of the fidelity susceptibility, order parameter, and entanglement entropy. Our results show that the DM interaction could influence the distribution of the regions of quantum phase transitions and cause different critical regions in the XY spin model. Meanwhile, the DM interaction has effective influence on the degree of entanglement of the system and could be used to increase the entanglement of the spin system.