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Register a new userThe entanglement in one-dimensional random XY spin chain with Dzyaloshinskii-Moriya interaction
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The impurities of exchange couplings, external magnetic fields and Dzyaloshinskii--Moriya (DM) interaction considered as Gaussian distribution, the entanglement in one-dimensional random $XY$ spin systems is investigated by the method of solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynamics at central locations of ferromagnetic and antiferromagnetic chains have been studied by varying the three impurities and the strength of DM interaction. (i) For ferromagnetic spin chain, the weak DM interaction can improve the amount of entanglement to a large value, and the impurities have the opposite effect on the entanglement below and above critical DM interaction. (ii) For antiferromagnetic spin chain, DM interaction can enhance the entanglement to a steady value. Our results imply that DM interaction strength, the impurity and exchange couplings (or magnetic field) play competing roles in enhancing quantum entanglement.
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Jordan-Wigner transformation and Bogolyubov transformation are the main steps of the diagonalization of Hamiltonian and paly an important role in the statistical mechanics calculations for one-dimensional Heisenberg spin chain model. Many methods can be exploited as a tool to detect quantum phase transition, regions of criticality and scaling behavior in the vicinity of a quantum phase transition, such as geometric phase, fidelity susceptibility, order parameter, and entanglement entropy, which have direct relation with Bogolyubov transformation. We diagonalized the Hamiltonian in XY spin-chain systems with Dzyaloshinskii-Moriya interactions, the results shows that only the energy spectrum but not the coefficients of the Bogolyubov transformation depends on DM interaction. Therefore, the DM interaction may not influence the critical magnetic field of quantum phase transitions and not induce new critical regions in the XY spin model. Moreover, we further prove the ideas by the methods of geometric phases in this model.
We investigate the entanglement of the ferromagnetic XY model in a random magnetic field at zero temperature and in the uniform magnetic field at finite temperatures. We use the concurrence to quantify the entanglement. We find that, in the ferromagnetic region of the uniform magnetic field $h$, all the concurrences are textit{generated} by the random magnetic field and by the thermal fluctuation. In one particular region of $h$, the next-nearest neighbor concurrence is generated by the random field but not at finite temperatures. We also find that the qualitative behavior of the maximum point of the entanglement in the random magnetic field depends on whether the variance of its distribution function is finite or not.
The thermal entanglement is investigated in a two-qubit Heisenberg XXZ system with Dzyaloshinskii-Moriya (DM) interaction. It is shown that the entanglement can be efficiently controlled by the DM interaction parameter and coupling coefficient $J_{z}$. $D_{x}$(the x-component parameter of the DM interaction) has a more remarkable influence on the entanglement and the critical temperature than $D_{z}$(the z-component parameter of the DM interaction). Thus, by the change of DM interaction direction, we can get a more efficient control parameter to increase the entanglement and the critical temperature.
Recently, there has been an increased interest in studying quantum entanglement and quantum coherence. Since both of these properties are attributed to the existence of quantum superposition, it would be useful to determine if some type of correlation between them exists. Hence, the purpose of this paper is to explore the type of the correlation in several systems with different types of anisotropy. The focus will be on the XY spin chains with the Dzyaloshinskii-Moriya interaction and the type of the mentioned bond will be explored using the quantum renormalization group method.
In this paper, we study the thermal entanglement in a two-qubit Heisenberg XYZ system with different Dzyaloshinskii-Moriya (DM) couplings. We show that different DM coupling parameters have different influences on the entanglement and the critical temperature. In addition, we find that when $J_{i}$ ($i$-component spin coupling interaction) is the largest spin coupling coefficient, $D_{i}$ ($i$-component DM interaction) is the most efficient DM control parameter, which can be obtained by adjusting the direction of DM interaction.
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