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arXiv:1709.03215 · Scientific Reports

Quantum coherence of the Heisenberg spin models with Dzyaloshinsky-Moriya interactions

Chandrashekar Radhakrishnan, Manikandan Parthasarathy, Segar Jambulingam, Tim Byrnes

Published Oct 18, 2017• 60 citations
arXivHTMLPDF

Abstract

Abstract We study quantum coherence in a spin chain with both symmetric exchange and antisymmetric Dzyaloshinsky-Moriya couplings. Quantum coherence is quantified using the recently introduced quantum Jensen-Shannon divergence, which has the property that it is easily calculable and has several desirable mathematical properties. We calculate exactly the coherence for arbitrary number of spins at zero temperature in various limiting cases. The σ z σ z interaction tunes the amount of coherence in the system, and the antisymmetric coupling changes the nature of the coherence. We also investigate the effect of non-zero temperature by looking at a two-spin system and find similar behavior, with temperature dampening the coherence. The characteristic behavior of coherence resembles that of entanglement and is opposite to that of discord. The distribution of the coherence on the spins is investigated and found that it arises entirely due to the correlations between the spins.

DOI
10.1038/s41598-017-13871-6

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arXiv:1109.5458•Sep 26, 2011•1 citation
Abstract We study quantum coherence in a spin chain with both symmetric exchange and antisymmetric Dzyaloshinsky-Moriya couplings. Quantum coherence is quantified using the recently introduced quantum Jensen-Shannon divergence, which has the property that it is easily calculable and has several desirable mathematical properties. We calculate exactly the coherence for arbitrary number of spins at zero temperature in various limiting cases. The σ z σ z interaction tunes the amount of coherence in the system, and the antisymmetric coupling changes the nature of the coherence. We also investigate the effect of non-zero temperature by looking at a two-spin system and find similar behavior, with temperature dampening the coherence. The characteristic behavior of coherence resembles that of entanglement and is opposite to that of discord. The distribution of the coherence on the spins is investigated and found that it arises entirely due to the correlations between the spins.
We study the dynamics of quantum discord and entanglement for two spin qubits coupled to a spin chain with Dzyaloshinsky—Moriya interaction. In the case of a two-qubit with an initial pure state, quantum correlations decay to zero at the critical point of the environment in a very short time. In the case of a two-qubit with initial mixed state, it is found that quantum discord may get maximized due to the quantum critical behavior of the environment, while entanglement vanishes under the same condition. Besides, we observed a sudden transition between classical and quantum decoherence when only a single qubit interacts with the environment. The effects of Dzyaloshinsky—Moriya interaction on quantum correlations are considered in the two cases. The decay of quantum correlations is always strengthened by Dzyaloshinsky—Moriya interaction.
Quantum coherence has played a decisive role in quantum information processing. On the other hand, quantum correlation can be considered as a powerful resource for delivering quantum information. Both quantum coherence and quantum correlation may occur in an information propagating process, which challenges us to understand the relationship between coherence and correlation. This is also an important procedure for physicists to know the features of quantum resources. Any quantum system interacting with its surrounding environment will destroy the quantum coherence and fail to fulfil any task of delivering quantum information. In this sense, studying the dynamics of quantum correlation and quantum coherence is very fascinating. In this paper, we investigate the dynamics of the quantum correlation and quantum coherence for two central qubits coupled to their own spin baths modeled by the XY spin chain with Dzyaloshinsky-Moriya interaction. We employ the quantum discord to characterize the quantum correlation, and use the relative entropy to measure quantum coherence. In this way the evolution law of the quantum discord and the relative entropy of quantum coherence of two-qubit system are derived, and the evolution law depends not only on the Dzyaloshinsky-Moriya interaction, the anisotropy parameter and the total number of spin chain sites, but also on the coupling strength between the central spin and its spin chain. Our findings are as follows. Firstly, we find that near the critical point of spin chain the quantum coherence abruptly changes, which can be used to detect the existence of quantum phase transition. Secondly, at the critical point, the relative entropy of quantum coherence is the same as that of classical correlation when time tt0, and it is the same as that of quantum discord when time tt0. At time t0, the sudden transition from quantum discord to classical correlation occurs. All in all, the relative entropy of quantum coherence reflects the behaviors of classical correlation and quantum discord for times tt0 and tt0, respectively, which is caused by the change of the optimal basis for quantum discord. Thirdly, the dynamics of quantum correlation and quantum coherence keep invariant under the scaling variation of the total number of spin chain sites and the coupling strength. Moreover, we find that all the Dzyaloshinsky-Moriya interactions and the anisotropy parameters, as well as the coupling strengths will enhance the decay of quantum coherence and quantum correlation, while they have no obvious effect on the relationship between dynamics of coherence and correlation. The above discussion reveals some new features of quantum coherence and quantum correlation, which may be useful in further developing quantum information theory.
The quantum coherence of one-dimensional planar spin models with Dzyaloshinsky-Moriya interaction is investigated. The anisotropic XY model, the isotropic XX model, and the transverse field model are studied in the large NNN limit using two qubit reduced density matrices and two point correlation functions. From our investigations we find that the coherence as measured using Jensen-Shannon divergence can be used to detect quantum phase transitions and quantum critical points. The derivative of coherence shows nonanalytic behavior at critical points, leading to the conclusion that these transitions are of second order. Further, we show that the presence of Dzyaloshinsky-Moriya coupling suppresses the phase transition due to residual ferromagnetism, which is caused by spin canting.
We consider the quantum correlations (entanglement and quantum discord) dynamics of two coupled spin qubits with Dzyaloshinsky-Moriya interaction influenced by a locally external magnetic field along zzz-direction and coupled to bath spin-1/2 particles as independent non-Markovian environment. We find that with increasing DzD_{z}Dz​ and decreasing JzJ_{z}Jz​, the value of entanglement and quantum discord increase for both antiferromagnetic and ferromagnetic materials. Not that, this growth is more for the ferromagnetic materials. In addition, we perceive that entanglement and quantum discord decrease with increased temperature and increased coupling constants between reduced system and bath. But, strong quantum correlations within the spins of bath reduce decoherence effects. We discuss about type of the constituent material of the central spins that it can speedup the quantum information processing and as a result, we perceive that one can improve and control the quantum information processing with correct selection of the properties of the reduced system (JJJ, JzJ_{z}Jz​, DzD_{z}Dz​).
We study the dynamics of quantum discord and entanglement for two spin qubits coupled to a spin chain with Dzyaloshinsky-Moriya (DM) interaction. We numerically and analytically investigate the time evolution of quantum discord and entanglement for two-qubit initially prepared in a class of X−X-X−structure state. In the case of evolution from a pure state, quantum correlations decay to zero in a very short time at the critical point of the environment. In the case of evolution from a mixed state, It is found that quantum discord may get maximized due to the quantum critical behavior of the environment while entanglement vanishes under the same condition. Moreover, we observed sudden transition between classical and quantum decoherence when single qubit interacts with the environment. The effects of DM interaction on quantum correlations are also considered and revealed in the two cases. It can enhance the decay of quantum correlations and its effect on quantum correlations can be strengthened by anisotropy parameter.