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Chinese Physics B

Critical entanglement and geometric phase of a two-qubit model with Dzyaloshinski–Moriya anisotropic interaction

Li Zhi-Jian, Xinlu Cheng, Wen Jiao-Jin

Published Jan 1, 2010• 3 citations
Publisher

Abstract

We consider a two-qubit system described by the Heisenberg XY model with Dzyaloshinski–Moriya (DM) anisotropic interaction in a perpendicular magnetic field to investigate the relation between entanglement, geometric phase and quantum phase transition (QPT). It is shown that the DM interaction has an effect on the critical boundary. The combination of entanglement and geometric phase may characterize QPT completely. Their jumps mean that the occurrence of QPT and inversely the QPT at the critical point at least corresponds to a jump of one of them.

DOI
10.1088/1674-1056/19/1/010305

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We consider a two-qubit system described by the Heisenberg XY model with Dzyaloshinski–Moriya (DM) anisotropic interaction in a perpendicular magnetic field to investigate the relation between entanglement, geometric phase and quantum phase transition (QPT). It is shown that the DM interaction has an effect on the critical boundary. The combination of entanglement and geometric phase may characterize QPT completely. Their jumps mean that the occurrence of QPT and inversely the QPT at the critical point at least corresponds to a jump of one of them.
We study the quantum entanglement and quantum phase transition (QPT) of the anisotropic spin-1/21/21/2 XYXYXY model with staggered Dzyaloshinskii-Moriya (DM) interaction by means of the quantum renormalization group method. The scaling of coupling constants and the critical points of the system are obtained. It is found that when the number of renormalization group iterations tends to infinity, the system exhibit a QPT between the spin-fluid and N\'eel phases which correspond with two saturated values of the concurrence for a given value of the strength of DM interaction. The DM interaction can enhance the entanglement and influence the QPT of the system. To gain further insight, the first derivative of the entanglement exhibit a nonanalytic behavior at the critical point and it directly associates with the divergence of the correlation length. This shows that the correlation length exponent is closely related to the critical exponent, i.e., the scaling behaviors of the system.
We study the effects of the Dzyaloshinski-Moriya (DM) anisotropic interaction on the ground-state properties of the Heisenberg XY spin chain by means of the fidelity susceptibility, order parameter, and entanglement entropy. Our results show that the DM interaction could influence the distribution of the regions of quantum phase transitions and cause different critical regions in the XY spin model. Meanwhile, the DM interaction has effective influence on the degree of entanglement of the system and could be used to increase the entanglement of the spin system.
We investigate the entanglement of a three-qubit anisotropic Heisenberg XXZ ring with Dzyaloshinskii–Moriya (DM) interaction in thermal equilibrium at temperature T in the presence of an external magnetic field B along the z-axis and obtain analytic expression for the concurrence, in which the dependence of the concurrence on the anisotropic coupling coefficient Jz, external magnetic field B, the DM interaction parameter D and temperature T is described. The DM interaction is found to have a more significant role than the others in increasing the critical temperature or the entanglement area. We also calculate the ground-state entanglement under various control parameters and give expressions for the quantum critical points at which quantum phase transition (QPT) takes place. These results show that one is able to produce, when it does not exist, or increase (up to some limit), when it exists, the concurrence so that the efficient control of entanglement by appropriate combinations of the tunable parameters may be possible.