Quantum entanglement as an important resource in quantum computation and quantum information has attracted much attention in recent decades. The effect of temperature should be viewed as an external control in the preparation of entangled state, and the thermal entanglement of the Heisenberg spin model has been discussed intensively. Due to the quantum fluctuation and thermal effect, there have been found some interesting physical phenomena in the geometrically frustrated spin system at zero or a certain temperature. Meanwhile, the lattice spin system with triangular plaquettes is regarded as a general structure of magnetic material. In this paper, we theoretically analyze the thermal entanglement of Ising-Heisenberg chain with triangular plaquettes. The transfer matrix method is used to calculate numerically the thermal entanglement in the infinite Ising-Heisenberg chain. We consider three kinds of Heisenberg spin interaction models (i.e., XXX-Heisenberg model, XXZ-Heisenberg model and XYZ-Heisenberg model), and discuss the effects of magnetic field and temperature on the three models, respectively. The results show that temperature and magnetic field have important effects on the three models. Meanwhile, it is found that the XXX-Heisenberg model is more sensitive than the anisotropy model (i.e., XXZ-Heisenberg model or XYZ-Heisenberg model) when temperature rises. A certain magnetic field would promote the generation of the quantum entangled states in all the three cases when the thermal fluctuation suppresses the quantum effects of the systems. In addition, it is found that the entanglement of XYZ-Heisenberg model is more robust than the others at a higher temperature, especially when the anisotropy along the z axis is greater than that along the y axis. We also plot the variations of the critical temperature with magnetic field in the three models. From the critical temperature-magnetic field phase diagrams, we can obtain the range of parameters in which the pairwise entanglement of the system exists. We also find that the entanglement revival behaviors may occur in a specific range of the parameters. Therefore, the properties of the thermal entanglement of Ising-Heisenberg chain with triangular plaquettes can be controlled and enhanced by choosing and using suitable parameters of magnetic field and temperature.
Project supported by the National Natural Science Foundation of China (Grant No. 11274102), the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-11-0960), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20134208110001).