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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.
[1] Bennett C H, Brassard C, Crépeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895
[2] Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881
[3] Ekert A K 1991 Phys. Rev. Lett. 67 661
[4] Arnesen M C, Bose S, Vedral V 2001 Phys. Rev. Lett. 87 017901
[5] Wang X G 2001 Phys. Rev. A 64 012313
[6] Wang X G 2001 Phys. Lett. A 281 101
[7] Zhang Y L, Zhou B 2011 Acta Phys. Sin. 60 120301 (in Chinese)[张英丽, 周斌 2011 物理学报 60 120301]
[8] Cao M, Zhu S Q 2005 Phys. Rev. A 71 034311
[9] Wang X G, Fu H C, Solomon A I 2001 J. Phys. A 34 11307
[10] Hou J M, Du L, Ding J Y, Zhang W X 2010 Chin. Phys. B 19 110313
[11] Wang Y H, Xia Y J 2009 Acta Phys. Sin. 58 7479 (in Chinese)[王彦辉, 夏云杰 2009 物理学报 58 7479]
[12] Hu Z N, Yi K S, Park K S 2007 J. Phys. A: Math. Theor. 40 7283
[13] Łuczak J, Bułka B R 2012 J. Phys.: Condens. Matter 24 375303
[14] Zhou B 2011 Int. J. Mod. Phys. B 25 2135
[15] Majumdar C K, Ghosh D K 1969 J. Math. Phys. 10 1388
[16] Majumdar C K, Ghosh D K 1969 J. Math. Phys. 10 1399
[17] Hase M, Terasaki I, Uchinokura K 1993 Phys. Rev. Lett. 70 3651
[18] Bray J W, Interrante L V, Jacobs L S, Bonner J C 1983 Extended Linear Chain Compounds (Volume 3) (New York: Plenum Press) pp353-415
[19] Gu S J, Li H, Li Y Q, Lin H Q 2004 Phys. Rev. A 70 052302
[20] Eryiǧit R, Gndç Y, Eryiǧit R 2006 Phys. Lett. A 358 363
[21] Eryiǧit R, Gndç Y, Eryiǧit R 2006 Phys. Lett. A 349 37
[22] Chhajlany R W, Tomczak P, Wójcik A, Richter J 2007 Phys. Rev. A 75 032340
[23] Liu R, Liang M L, Yuan B 2007 Eur. Phys. J. D 41 571
[24] Eryiǧit R 2009 Int. J. Theor. Phys. 48 885
[25] Kwek L C, Takahashi Y, Choo K W 2009 J. Phys.: Conf. Ser. 143 012014
[26] Şahintaş A, Akyz C 2016 Physica A 448 10
[27] Hill S, Wootters W K 1997 Phys. Rev. Lett. 78 5022
[28] Wootters W K 1998 Phys. Rev. Lett. 80 2245
[29] Coffman V, Kundu J, Wootters W K 2000 Phys. Rev. A 61 052306
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[1] Bennett C H, Brassard C, Crépeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895
[2] Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881
[3] Ekert A K 1991 Phys. Rev. Lett. 67 661
[4] Arnesen M C, Bose S, Vedral V 2001 Phys. Rev. Lett. 87 017901
[5] Wang X G 2001 Phys. Rev. A 64 012313
[6] Wang X G 2001 Phys. Lett. A 281 101
[7] Zhang Y L, Zhou B 2011 Acta Phys. Sin. 60 120301 (in Chinese)[张英丽, 周斌 2011 物理学报 60 120301]
[8] Cao M, Zhu S Q 2005 Phys. Rev. A 71 034311
[9] Wang X G, Fu H C, Solomon A I 2001 J. Phys. A 34 11307
[10] Hou J M, Du L, Ding J Y, Zhang W X 2010 Chin. Phys. B 19 110313
[11] Wang Y H, Xia Y J 2009 Acta Phys. Sin. 58 7479 (in Chinese)[王彦辉, 夏云杰 2009 物理学报 58 7479]
[12] Hu Z N, Yi K S, Park K S 2007 J. Phys. A: Math. Theor. 40 7283
[13] Łuczak J, Bułka B R 2012 J. Phys.: Condens. Matter 24 375303
[14] Zhou B 2011 Int. J. Mod. Phys. B 25 2135
[15] Majumdar C K, Ghosh D K 1969 J. Math. Phys. 10 1388
[16] Majumdar C K, Ghosh D K 1969 J. Math. Phys. 10 1399
[17] Hase M, Terasaki I, Uchinokura K 1993 Phys. Rev. Lett. 70 3651
[18] Bray J W, Interrante L V, Jacobs L S, Bonner J C 1983 Extended Linear Chain Compounds (Volume 3) (New York: Plenum Press) pp353-415
[19] Gu S J, Li H, Li Y Q, Lin H Q 2004 Phys. Rev. A 70 052302
[20] Eryiǧit R, Gndç Y, Eryiǧit R 2006 Phys. Lett. A 358 363
[21] Eryiǧit R, Gndç Y, Eryiǧit R 2006 Phys. Lett. A 349 37
[22] Chhajlany R W, Tomczak P, Wójcik A, Richter J 2007 Phys. Rev. A 75 032340
[23] Liu R, Liang M L, Yuan B 2007 Eur. Phys. J. D 41 571
[24] Eryiǧit R 2009 Int. J. Theor. Phys. 48 885
[25] Kwek L C, Takahashi Y, Choo K W 2009 J. Phys.: Conf. Ser. 143 012014
[26] Şahintaş A, Akyz C 2016 Physica A 448 10
[27] Hill S, Wootters W K 1997 Phys. Rev. Lett. 78 5022
[28] Wootters W K 1998 Phys. Rev. Lett. 80 2245
[29] Coffman V, Kundu J, Wootters W K 2000 Phys. Rev. A 61 052306
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