Some new Hamiltonians are constructed via the unitary Yang-Baxter matrices [Formula: see text] acting on a Hamiltonian H0 which describes nearest spin-spin interaction. By the concept of concurrence, we explore the thermal entanglement of these systems. We find that the interaction of z-component of two neighboring spins g has great influences on the thermal entanglement. It not only influences the critical temperature Tc, but can also influence the critical magnetic field Bc.
THERMAL ENTANGLEMENT IN THE TWO-QUBIT SYSTEMS CONSTRUCTED FROM THE YANG-BAXTER Rˇ-MATRIX
Some new Hamiltonians are constructed via the unitary Yang-Baxter matrices [Formula: see text] acting on a Hamiltonian H0 which describes nearest spin-spin interaction. By the concept of concurrence, we explore the thermal entanglement of these systems. We find that the interaction of z-component of two neighboring spins g has great influences on the thermal entanglement. It not only influences the critical temperature Tc, but can also influence the critical magnetic field Bc.
We elucidate the finite temperature entanglement properties of N=9 qubits Heisenberg XX and XXZ models under the presence of a polarized magnetic field in xz plane by means of concurrence concept. We perform a systematic analysis for a wide range of the system parameters. Our results suggest that the global phase regions which separate the entangled and non-entangled regions sensitively depend upon the spin-spin interaction term of the z− component of two neighboring spins Jz/Jx, temperature as well as polarized magnetic field components. Thereby, we think that polarized magnetic field can be used a control parameter to determine the amount of thermal entanglement between pair of qubits for different temperatures and spin-spin interaction terms. Moreover, it has been found that the nearest-neighbor pair of qubits does not point out a re-entrant type entanglement character when one only deals with the nearest-neighbor pair of qubits. However, as one considers next-nearest neighbor pair of qubits, it is possible to see the evidences of re-entrant type entanglement behaviors.
Quantum thermal entanglement of two next nearest-neighbor qubits in a four-qubit isotropic Heisenberg XY model consisting of spin 1/2 and spin S in a homogeneous external magnetic field B was investigated by concurrence measure of entanglement.The results show that the external magnetic field can induce the thermal entanglement of two next nearest-neighbor qubits.The amplitude of thermal entanglement is dependent on the spin S,temperature T and homogeneous external magnetic field B.As a result,it is feasible to control thermal entanglement by adjusting the value of external magnetic field B.When S is sufficiently large,the threshold temperature above which there is no thermal entanglement may also be very high.The feature can be used in high-temperature entanglement of condensed matter systems and it will be useful in the research of quantum information in solid systems.
In the study of thermal entanglement of the Heisenberg spin chain model, one usually considers only the spin interaction between the nearest neighboring qubits. Actually, a generalized Heisenberg model, so-called J1-J2 Heisenberg model, which is constructed by considering the fact that not only the nearest neighboring but also the next nearest neighboring spin interaction also plays an important role. In J1-J2 Heisenberg model, due to the next nearest neighboring spin interaction, the frustration effect can occur and has an important influence on the magnetic properties of the model. In this paper we investigate the thermal entanglement of a five-qubit XXZ Heisenberg spin chain with the next nearest neighboring interaction in a magnetic field. Using the numerical method, we calculate the pairwise concurrences of the nearest neighbouring qubits and the next nearest neighboring qubits, abbreviated as C12 and C13 respectively. The numerical results show that the frustration parameter α has an important effect on the pairwise thermal entanglement. Moreover, C12 and C13 have different variations with the change of the frustration parameter α. Meanwhile, it is found that the temperature, magnetic field, Dzyaloshinkii-Moriya (DM) interaction and anisotropic parameter also have great effects on the thermal entanglement. The increasing of temperature can reduce the thermal entanglement. The magnetic field can enhance the thermal entanglement between both two nearest and next nearest neighboring qubits, but when the magnetic field becomes strong enough, only the thermal entanglement between the two nearest neighboring qubits is suppressed. A certain extent of DM interaction can enhance the thermal entanglement between the two nearest neighboring qubits. But for the next nearest neighboring qubits, without the magnetic field, the increasing of DM interaction mainly enlarge the entanglement vanishing area of frustration parameter α. When the system changes from anisotropic to isotropic state, the entanglement vanishing area also changes obviously for C12 and C13. Thus, we can choose appropriate magnetic field strength, temperature, frustration parameter, DM interaction parameter and anisotropic parameter to effectively control and enhance the thermal entanglement of the system.
The thermal entanglement in the Heisenberg XYZ chain is investigated in the presence of an external magnetic field B. In the two-qubit system, the critical magnetic field Bc is increased by introducing the interaction of the z component of two neighboring spins Jz. This interaction not only improves the critical temperature Tc, but also enhances the entanglement for a particular fixed B. We also analyze the pairwise entanglement between nearest neighbors in three qubits. The pairwise entanglement, for a fixed T, can become strong by controlling B and Jz.
In this paper, we study the property of thermal entanglement in four-qubit Heisenberg model, where Dzyaloshinskii-Moriya (DM) interaction is considered, and investigate the pairwise concurrences of two nearest-neighbor qubits and two next-neighbor qubits to study this entanglement property. The result shows that for the two-next-neighbor-qubit case, there exists pairwise concurrence neigher in ferromagnetic model nor in antiferromagnetic model; but for the two-nearest-neighbor-qubits case, the DM interaction and the parameter of the anisotropy exchange coupling have a significant influence on the pairwise entanglement and critical temperature Tc. Moreover, the pairwise concurrence will decrease with the increase of temperature. When the temperature execeds its critical value, the pairwise concurrence disappears. Therefore, the pairwise entanglement can be controlled and enhanced by choosing the appropriate parameters of the DM interaction and the anisotropy exchange coupling.
In this paper, we investigate the role of Dzyaloshinski–Moriya (DM) interaction in the pairwise entanglement in the three- and four-qubit XX models with magnetic field. In the four-qubit model, the pairwise entanglements of two nearest-neighbor qubits and two next-neighbor qubits are investigated, respectively. The dependences of the critical temperature at which the pairwise thermal entanglement disappears on DM interaction and magnetic fields are studied in details. At zero temperature, the entanglement can undergo sudden changes with adjustment of the parameters, and the general results of the concurrence are obtained in all cases.