In this paper the effect of Dzyaloshinskii-Moriya interaction and anisotropy on the entanglement of Heisenberg chain has been studied. While the anisotropy suppresses the entanglement due to favoring of the alignment of spins, the DM interaction restores the spoiled entanglement via creation of the quantum fluctuations. Thermodynamic limit of the model and emerging of nonanalytic behavior of the entanglement have also been probed. The singularities of the entanglement correspond to the critical boundary separating different phases of the model. The singularity of the entanglement derivative approaches the critical point from the gapped phase and will be symmetric if both phases on the boundary are gapped.
In this paper the effect of Dzyaloshinskii-Moriya interaction and anisotropy on the entanglement of Heisenberg chain has been studied. While the anisotropy suppresses the entanglement due to favoring of the alignment of spins, the DM interaction restores the spoiled entanglement via creation of the quantum fluctuations. Thermodynamic limit of the model and emerging of nonanalytic behavior of the entanglement have also been probed. The singularities of the entanglement correspond to the critical boundary separating different phases of the model. The singularity of the entanglement derivative approaches the critical point from the gapped phase and will be symmetric if both phases on the boundary are gapped.
By using the density-matrix renormalization group method, the spin entanglement in the antiferromagnetic Heisenberg chain with the staggered Dzyaloshinskii-Moriya (DM) interactions is investigated. It is found that the staggered DM interactions remove the field-induced second order quantum phase transition of the system at the magnitude of magnetic field H＝2, and lead to the vanishing of the anomalous behavior of quantum entanglement. Also, the staggered DM interactions eliminate the divergence of entanglement range. It means the disappearance of the factorizing point in the model studied. Due to the presence of the staggered DM interactions, the system will never come to the state of saturated ferromagnetism under finite magnetic fields, thus maintaining the spin entanglement. The staggered DM interactions favor the tuning of the strength and range of spin entanglement.
In this paper, we study the improvement and manipulation of pairwise thermal entanglement in one-dimentional three-qubit Heisenberg model, where Dzyaloshinskii-Moriya （DM） interaction is considered and concurrence is calculated to research this entanglements property. The results show that for XXX model, DM interaction can induce entanglement in the antiferromagnetic and ferromagnetic spin chains although the required critical values are different for these cases. For XXZ model, by introducing DM interaction D, antiferromagnetic spin chain has entanglement which is absent when D=0, and in addition, for antiferromagnetic and ferromagnetic cases, DM interaction D and the anisotropy parameter Δ have different effects on entanglement. As a result, the entanglement can be controlled and enhanced by choosing appropriate DM interaction and anisotropy parameter. Furthermore, we find that at the same temperature, no matter for antiferromagnetic or ferromagnetic spin chains, the critical DM interaction inducing entanglement should be greater in a three-qubit XXZ model than that in a two-qubit XXZ model.
In this paper, we address the tripartite quantum discord for the Heisenberg XY chain with the Dzyaloshinskii–Moriya (DM) interaction using the quantum renormalization-group (QRG) method. In thermodynamic limit, like the entanglement, the tripartite discord exhibits the quantum phase transition (QPT) between the spin-fluid and the Neel phases. The effect of the DM interaction and the anisotropy on the features of the tripartite quantum discord has been probed. It is noted that the DM interaction brings the critical point earlier and affects heavily with the size of the system. Moreover, the system requires a larger number of the iterations to achieve the QPT for the tripartite quantum discord as compared to the entanglement.
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.
Thermal entanglement of a(1/2,1) mixed-spin Heisenberg XXZ model in the presence of Dzyaloshinski-Moriya(DM) interaction and anisotropy Δ is investigated.It is shown that the thermal entanglement and the critical temperature can be efficiently controlled by adjusting the DM interaction parameter and anisotropy coefficient Δ.Thus,by changing the values of DM interaction and anisotropy coefficient Δ,we can get a more efficient control parameter to increase the entanglement and expand the steady value region to slow down the decreace of the entanglement.
We investigate the thermal entanglement in a spin-1/2 Ising–Heisenberg diamond chain, in which the vertical Heisenberg spin dimers alternate with single Ising spins. Due to the fact that the Dzyaloshinskii–Moriya (DM) interaction contributes to unusual and interesting magnetic properties in actual materials, and moreover it plays a significant role in the degree of the entanglement of the Heisenberg quantum spin systems, we focus on the effects of different DM interactions, including D z and D x , on the thermal entanglement of the Heisenberg spin dimer. The concurrence, as a measure of spin dimer entanglement, is calculated for different values of exchange interactions, DM interaction, external magnetic field, and temperature. It is found that the critical temperature and the critical magnetic field corresponding to the vanishing of entanglement increase with DM interaction, and the entanglement revival region gets larger by increasing DM interaction, thus DM interaction favors the formation of the thermal entanglement. It is observed that different DM interaction parameters ( D z and D x ) have remarkably different influences on the entanglement. Different from the case D z , there is the non-monotonic variation of the concurrence with temperature in the case D x , and additionally the DM interaction D x can induce the entanglement near zero temperature in the case that the antiferromagnetic Ising-type interaction constant is larger than the antiferromagnetic Heisenberg interaction constant. It is also shown that for the same value of DM interaction the critical magnetic field of the case D x is larger than that of the case D z .