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研究了具有三角自旋环的伊辛-海森伯链在磁场作用下的热纠缠性质.分别讨论了三角自旋环中自旋1/2粒子间相互作用的三种情形，即XXX，XXZ和XYZ海森伯模型.利用转移矩阵方法，数值计算了具有三角自旋环的伊辛-海森伯链的配对纠缠度.计算结果表明，外加磁场强度和温度对系统处于上述三种海森伯模型的热纠缠性质均有重要影响.给出了系统在不同的海森伯模型下，纠缠消失对应的临界温度随磁场强度的变化图，由此可以得到系统存在配对纠缠的参数区域，同时发现在特定的参数区域存在纠缠恢复现象.因此适当调节温度和磁场强度，可以有效调控具有三角自旋环的伊辛-海森伯链热纠缠性质.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.
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Keywords:
- thermal entanglement /
- pairwise concurrence /
- Ising-Heisenberg chain /
- transfer matrix approach
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[1] Misguich G, Lhuillier C 2004 Frustrated Spin Systems (Singapore:World Scientific) p229
[2] Lee S H, Kikuchi H, Qiu Y, Lake B, Huang Q, Habicht K, Kiefer K 2007 Nature Mater. 6 853
[3] Moessner R, Sondhi S L 2001 Phys. Rev. B 63 224401
[4] Schmidt B, Shannon N, Thalmeier P 2006 J. Phys.:Conf. Ser. 51 207
[5] Zhitomirsky M E, Honecker A, Petrenko O A 2000 Phys. Rev. Lett. 85 3269
[6] Lee S, Lee K C 1998 Phys. Rev. B 57 8472
[7] Choi K Y, Matsuda Y H, Nojiri H, Kortz U, Hussain F, Stowe A C, Ramsey C, Dalal N S 2006 Phys. Rev. Lett. 96 107202
[8] Trif M, Troiani F, Stepanenko D, Loss D 2008 Phys. Rev. Lett. 101 217201
[9] Kubo K 1993 Phys. Rev. B 48 10552
[10] Nakamura T, Saika Y 1995 J. Phys. Soc. Jpn. 64 695
[11] Nakamura T, Kubo K 1996 Phys. Rev. B 53 6393
[12] Chen S, Bttner H, Voit J 2003 Phys. Rev. B 67 054412
[13] Guo Y P, Liu Z Q, Xu Y L, Kong X M 2016 Phys. Rev. E 93 052151
[14] Collins M F, Petrenko O A 1997 Can. J. Phys. 75 605
[15] Lecheminant P, Bernu B, Lhuillier C, Pierre L, Sindzingre P 1997 Phys. Rev. B 56 2521
[16] Waldtmann C, Everts H U, Bernu B, Lhuillier C, Sindzingre P, Lecheminant P, Pierre L 1998 Eur. Phys. J. B 2 501
[17] Mila F 1998 Phys. Rev. Lett. 81 2356
[18] Mambrini M, Trébosc J, Mila F 1999 Phys. Rev. B 59 13806
[19] Totsuka K, Mikeska H J 2002 Phys. Rev. B 66 054435
[20] Rojas O, Alcaraz F C 2003 Phys. Rev. B 67 174401
[21] Rojas O, Rojas M, Ananikian N S, de Souza S M 2012 Phys. Rev. A 86 042330
[22] Abgaryan V S, Ananikian N S, Ananikyan L N, Hovhannisyan V V 2015 Solid State Commun. 224 15
[23] Baxter R J 1982 Exactly Solved Models in Statistical Mechanics (New York:Academic Press) p89
[24] Hida K 1994 J. Phys. Soc. Jpn. 63 2359
[25] Ohanyan V, Ananikian N S 2003 Phys. Lett. A 307 76
[26] Strečka J, Hagiwara M, Jaščur M, Minami K 2004 Czech. J. Phys. 54 583
[27] Strečka J, Jaščur M, Hagiwara M, Minami K, Narumi Y, Kindo K 2005 Phys. Rev. B 72 024459
[28] Antonosyan D, Bellucci S, Ohanyan V 2009 Phys. Rev. B 79 014432
[29] Ohanyan V 2010 Phys. Atom. Nucl. 73 494
[30] Arnesen M C, Bose S, Vedral V 2001 Phys. Rev. Lett. 87 017901
[31] Wang X 2001 Phys. Rev. A 64 012313
[32] Wang X 2001 Phys. Lett. A 281 101
[33] Kamta G L, Starace A F 2002 Phys. Rev. Lett. 88 107901
[34] Zhou L, Song H S, Guo Y Q, Li C 2003 Phys. Rev. A 68 024301
[35] Gunlycke D, Kendon V M, Vedral V, Bose S 2001 Phys. Rev. A 64 042302
[36] Terzis A F, Paspalakis E 2004 Phys. Lett. A 333 438
[37] Canosa N, Rossignoli R 2004 Phys. Rev. A 69 052306
[38] Xi X Q, Chen W X, Hao S R, Yue R H 2002 Phys. Lett. A 300 567
[39] Sun Y, Chen Y, Chen H 2003 Phys. Rev. A 68 044301
[40] Asoudeh M, Karimipour V 2005 Phys. Rev. A 71 022308
[41] Cao M, Zhu S 2005 Phys. Rev. A 71 034311
[42] Zhang G F, Li S S 2005 Phys. Rev. A 72 034302
[43] Wu K D, Zhou B, Cao W Q 2007 Phys. Lett. A 362 381
[44] Zhou B 2011 Int. J. Mod. Phys. B 25 2135
[45] Chen S R, Xia Y J, Man Z X 2010 Chin. Phys. B 19 050304
[46] Ren J Z, Shao X Q, Zhang S, Yeon K H 2010 Chin. Phys. B 19 100307
[47] Lu P, Wang J S 2009 Acta Phys. Sin. 58 5955 (in Chinese)[卢鹏, 王顺金 2009 58 5955]
[48] Zhang Y L, Zhou B 2011 Acta Phys. Sin. 60 120301 (in Chinese)[张英丽, 周斌 2011 60 120301]
[49] Ananikian N S, Ananikyan L N, Chakhmakhchyan L A, Rojas O 2012 J. Phys.:Condens. Matter 24 256001
[50] Torrico J, Rojas M, de Souza S M, Rojas O, Ananikian N S 2014 Europhys. Lett. 108 50007
[51] Abgaryan V S, Ananikian N S, Ananikyan L N, Hovhannisyan V 2015 Solid State Commun. 203 5
[52] Qiao J, Zhou B 2015 Chin. Phys. B 24 110306
[53] Hill S, Wootters W K 1997 Phys. Rev. Lett. 78 5022
[54] Wootters W K 1998 Phys. Rev. Lett. 80 2245
[55] Coffman V, Kundu J, Wootters W K 2000 Phys. Rev. A 61 052306
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