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Journal of Atomic and Molecular Physics

Entanglement properties of XX model with three spin interactions

Xiu Zhang

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

Using the Concurrence criterion,we investigate the entanglement properties of XX model with three spin interactions.The effects of the three spin interaction J_2 and temperature T on the entanglement are discussed in both ferromagnetic and anti-ferromagnetic cases.Our results show that J_2 enhances the entanglement of the system,but the extent is difference for ferromagnetic and anti-ferromagnetic cases.J_2 also affects the critical temperature T_C,at which the entanglement disappears.T_C decreases with the increasing of J_2.Moreover,our results also indicate that the maximal entanglement increases with the decreasing of system temperature T.In addition,we also investigate the pairwise entanglement of the eigenstates of the Hamiltonian and discuss the ground-state entanglement.We obtain the quantum critical point at which the quantum phase transition takes place.

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Using the Concurrence criterion,we investigate the entanglement properties of XX model with three spin interactions.The effects of the three spin interaction J_2 and temperature T on the entanglement are discussed in both ferromagnetic and anti-ferromagnetic cases.Our results show that J_2 enhances the entanglement of the system,but the extent is difference for ferromagnetic and anti-ferromagnetic cases.J_2 also affects the critical temperature T_C,at which the entanglement disappears.T_C decreases with the increasing of J_2.Moreover,our results also indicate that the maximal entanglement increases with the decreasing of system temperature T.In addition,we also investigate the pairwise entanglement of the eigenstates of the Hamiltonian and discuss the ground-state entanglement.We obtain the quantum critical point at which the quantum phase transition takes place.
The entanglement properties of a three-spin XXZ Heisenberg chain with three-spin interaction are studied by means of concurrence of pairwise entanglement. We show that ground-state pairwise entanglement, pairwise thermal entanglement, or quantum phase transition is not present in antiferromagnetic spin chain. For the ferromagnetic case, quantum phase transition takes place at Δ = 1 for anisotropic interaction and at some values of three-spin coupling strength, and pairwise thermal entanglement increases when the value of J / T increases and with anisotropic interaction and three-spin interaction decrease. In addition, we find that increasing the anisotropic interaction and the three-spin interaction will decrease critical temperature.
Using the method of Negativity the entangle properties of the mixed-spin XXZ model with crystal field were studied.The influence of the temperature,the crystal field interaction and the anisotropic interaction to the entanglement were discussed.The results showed that the maximal entanglement increase with the decrease of the temperature.Both the crystal field d and the anisotropic Δ decrease the maximal entanglement of the system.But the critical temperature of entanglement TC and the maximal entanglement temperature Tmaxwere enhanced by d and Δ.
We studied the properties of thermal entanglement in one-dimention two-qubit Heisenberg model,where Dzyaloshinskii-Moriya(DM) interaction between spin with x-component and y-component was considered and concurrence was calculated to research this entanglement property.The results showed that on the case of ferromagnetic and antiferromagnetic,interaction had different effects on the entanglement and critical temperature.Therefore,the entanglement could be controlled and enhanced by choosing appropriate interaction between x-component and y-component.
The pairwise entanglement of the Heisenberg XX chain with next-nearest-neighbor (NNN) interactions was investigated by using the concurrence measure. The results show that for the nearest-neighbor sites, the entanglement may be improved or suppressed depending on the magnitudes of the NNN coupling constant J, while for the next-nearest-neighbor sites, it always increases with the increase of |J|. The critical temperature Tc decreases with the increase of J for the nearest-neighbor entanglement and increases with the increase of |J| for the next-nearest-neighbor entanglement, respectively. We also show that the general Heisenberg XX model still can be used to create the entangled W states of three and four qubits, and that the presence of NNN coupling has no effect on the creation of four-qubit W states, while it shifts the instant of time at which the three-qubit W states are created.
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 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.