Bipartite entanglement in spin-1/2 Heisenberg model

HU Ming-Liang; TIAN Dong-Ping

doi:10.1088/1674-1137/32/4/013

Chinese Physics C> 2008, Vol. 32> Issue(4) : 303-307 DOI: 10.1088/1674-1137/32/4/013

Bipartite entanglement in spin-1/2 Heisenberg model

HU Ming-Liang ^, ,
TIAN Dong-Ping

Abstract
HTML
Reference
Related

PDF

Abstract：
The bipartite entanglement of the two- and three-spin Heisenberg model was investigated by using the concept of negativity. It is found that for the ground-state entanglement of the two-spin model, the negativity always decreases as B increases if Δ<γ－1, and it may keep a steady value of 0.5 in the region of B<J[(Δ+1)²－γ²]^1/2if Δ>γ－1, while for that of the three-spin model, the negativity exhibits square wave structures if γ=0 or Δ=0. For thermal states, there are two areas showing entanglement, namely, the main region and the sub-region. The main region exists only when Δ>Δ_c (Δ_c=γ－1 and (γ²－1)/2 for the 2- and 3-spin model respectively) and extends in terms of B and T as Δ increases, while the sub-region survives only when γ≠0 and shrinks in terms of B and T as Δ increases.

References

[1]

. Ekert A K. Phys. Rev. Lett., 1991, 67(6): 661-6632. Bennett C H, Brassard G, Crépeau C et al. Phys. Rev.Lett., 1993, 70: 1895-18993. DiVincenzo D P et al. Nature, 2000, 408: 339-3424. Bennett C H, Wiesner S J. Phys. Rev. Lett., 1992, 69(20):2881-28845. Bennett C H, DiVincenzo D P. Nature, 2000, 404: 2476. Arnesen M C, Bose S, Vedral V. Phys. Rev. Lett., 2001,87: 0179017. Kamta G L, Starace A F. Phys. Rev. Lett., 2002, 88:1079018. WANG X G. Phys. Rev. A, 2001, 64: 0123139. WANG X G. Phys. Rev. A, 2002, 66: 04430510. ZHOU L et al. Phys. Rev. A, 2003, 68: 02430111. SUN Y et al. Phys. Rev. A, 2003, 68: 04430112. Asoudeh M, Karimipour V. Phys. Rev. A, 2005, 71: 02230813. CAO M, ZHU S Q. Phys. Rev. A, 2005, 71: 03431114. ZHANG G F, LI S S. Phys. Rev. A, 2005, 72: 03430215. WANG X G. Phys. Lett. A, 2001, 281: 101-10416. WANG X G, Zanardi P. Phys. Lett. A, 2002, 301: 1-617. HU Ming-Liang, TIAN Dong-Ping. Science in China G,2007, 50(2): 208-21418. HU Ming-Liang, TIAN Dong-Ping. HEP NP, 2006,30(11): 1132-113619. TIAN Dong-Ping, HU Ming-Liang. HEP NP, 2007,31(5): 509-51220. Venuti L C, Boschi C D E, Roncaglia M. Phys. Rev. Lett.,2006, 96: 24720621. XI Xiao-Qiang, HAO San-Ru, CHEN Wen-Xue et al. Phys.Lett. A, 2002, 297: 291-29922. WANG X G. Phys. Rev. E, 2004, 69: 06611823. WANG X G et al. J. Phys. A, 2005, 38: 870324. SUN Z, WANG X G, LI Y Q. New. J. Phys., 2005, 7: 8325. WANG X G, WANG Z D. Phys. Rev. A, 2006, 73: 06430226. Canosa N, Rossignoli R. Phys. Rev. A, 2006, 73: 02234727. ZHANG Jing-Fu, LONG Gui-Lu, ZHANG Wei et al. Phys.Rev. A, 2005, 72: 01233128. ZHANG Yong, LIU Dan, LONG Gui-Lu. Chin. Phys., 2007,16: 324-32829. LIU Dan et al. Chin. Phys. Lett., 2007, 24: 8-1030. ZHANG Yong, LONG Gui-Lu, WU Yu-Chun et al. Commun. Theor. Phys., 2007, 47: 787-79031. Bose S. Phys. Rev. Lett., 2003, 91: 20040332. Christandl M, Datta N, Ekert A et al. Phys. Rev. Lett.,2004, 92: 18790233. Subrahmanyam V. Phys. Rev. A, 2004, 69: 03430434. Benjamin S C, Bose S. Phys. Rev. Lett., 2003, 90: 24790135. Loss D, DiVincenzo D P. Phys. Rev. A, 1998, 57: 120-12636. Vidal G, Werner R F. Phys. Rev. A, 2002, 65: 032314

[1]	Zhi Yang , Ling-Yan Hung . Exploring the entanglement of free spin-${\bf\dfrac{1}{2}}$, spin-1 and spin-2 fields. Chinese Physics C, 2019, 43(5): 053102. doi: 10.1088/1674-1137/43/5/053102
[2]	Yi Ling;Meng-He Wu;Yikang Xiao . Entanglement in simple spin networks with a boundary. Chinese Physics C, 2019, df87c41e-622f-49a7-b081-5c584df157aa(11): 13106-.
[3]	Hui Li , Zong-Xiu Wu , Chun-Sheng An , Hong Chen . Low-lying 1/2^- hidden strange pentaquark states in the constituent quark model. Chinese Physics C, 2017, 41(12): 124104. doi: 10.1088/1674-1137/41/12/124104
[4]	ZHU Jing-Min . Quantum phase transitions in matrix product states of one-dimensional spin-1 chains. Chinese Physics C, 2014, 38(10): 103102. doi: 10.1088/1674-1137/38/10/103102
[5]	ZHU Jing-Min . Quantum phase transitions in matrix product states ofone-dimensional spin-1/2 chains. Chinese Physics C, 2014, 38(12): 123102. doi: 10.1088/1674-1137/38/12/123102
[6]	QIN Meng , WANG Xiao , LI Yan-Biao , BAI Zhong , LIN Shang-Jin . Effects of inhomogeneous magnetic fields and different Dzyaloshinskii-Moriya interaction on entanglement and teleportation in a two-qubit Heisenberg XY Z chain. Chinese Physics C, 2013, 37(11): 113102. doi: 10.1088/1674-1137/37/11/113102
[7]	ZHU Jing-Min . The entanglement property in matrix product spin systems. Chinese Physics C, 2012, 36(4): 311-315. doi: 10.1088/1674-1137/36/4/003
[8]	ZHENG Qiang , ZHI Qi-Jun , ZHANG Xiao-Ping , REN Zhong-Zhou . Controllable entanglement sudden birth of Heisenberg spins. Chinese Physics C, 2011, 35(2): 135-138. doi: 10.1088/1674-1137/35/2/005
[9]	LIU Xiang . Derivation of a 1/r² potential term for QQ in a potential model. Chinese Physics C, 2010, 34(9): 1482-1484. doi: 10.1088/1674-1137/34/9/078
[10]	QIN Meng , LI Yan-Biao , BAI Zhong , LIN Shang-Jin , LIU Wei . Entanglement in a two-qubit Heisenberg XXZ chain with different Dzyaloshinskii-Moriyacouplings and an inhomogeneous magnetic field. Chinese Physics C, 2010, 34(11): 1693-1695. doi: 10.1088/1674-1137/34/11/004
[11]	QIN Meng , LI Yan-Biao . Effect of spin-orbit interaction on entanglement of two-qutrit Heisenberg XYZ systems in an inhomogeneous magnetic field. Chinese Physics C, 2010, 34(4): 448-451. doi: 10.1088/1674-1137/34/4/005
[12]	. Lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments in chiral perturbation theory. Chinese Physics C, 2010, 34(9): 1307-1311. doi: 10.1088/1674-1137/34/9/030
[13]	YUAN Yi , LI Kang , WANG Jian-Hua , CHEN Chi-Yi . Spin-1/2 relativistic particle in a magnetic field in NC phase space. Chinese Physics C, 2010, 34(5): 543-547. doi: 10.1088/1674-1137/34/5/005
[14]	QIN Meng , TIAN Dong-Ping . Bipartite entanglement in a two-qubit Heisenberg XXZ chain under aninhomogeneous magnetic field. Chinese Physics C, 2009, 33(4): 249-251. doi: 10.1088/1674-1137/33/4/002
[15]	TIAN Dong-Ping , HU Ming-Liang . Dynamics of Multipartite Entanglement in the Heisenberg Model. Chinese Physics C, 2007, 31(5): 509-512.
[16]	TAO Ying-Juan , HU Ming-Liang , TIAN Dong-Ping , QIN Meng . Global Bipartite Entanglement in the Three-Qubit Heisenberg XXX Spin Chain with Impurity. Chinese Physics C, 2007, 31(10): 990-994.
[17]	TIAN Dong-Ping , QIN Meng , TAO Ying-Juan , HU Ming-Liang . Impurity Entanglement in Spin-1 Heisenberg XX Chain. Chinese Physics C, 2007, 31(11): 1082-1085.
[18]	ZHAO Xiu-Mei , CAO Li-Ke , YANG Tao , YUE Rui-Hong . Integrability of a Quantum Derivative Nonlinear Schrodinger Model for Spin-1/2 Particle. Chinese Physics C, 2004, 28(9): 936-940.
[19]	Gao Xiaochun , Xu Donghui . Removability of the Topological Term in the 2+1 Dimensional CP¹ Model. Chinese Physics C, 1995, 19(S3): 257-264.
[20]	Sun Changpu , Pang Lin , Ge Molin . Effective Topological Action in Heisenberg Spin Model as Berry's Phase. Chinese Physics C, 1992, 16(S1): 51-56.

Access

Get Citation

HU Ming-Liang and TIAN Dong-Ping. Bipartite entanglement in spin-1/2 Heisenberg model[J]. Chinese Physics C, 2008, 32(4): 303-307. doi: 10.1088/1674-1137/32/4/013

HU Ming-Liang and TIAN Dong-Ping. Bipartite entanglement in spin-1/2 Heisenberg model[J]. Chinese Physics C, 2008, 32(4): 303-307. doi: 10.1088/1674-1137/32/4/013 shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2007-07-16
Revised: 2007-11-16

Article Metric

Article Views(3880)
PDF Downloads(669)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Bipartite entanglement in spin-1/2 Heisenberg model

Corresponding author: HU Ming-Liang,

Received Date: 2007-07-16

Accepted Date: 2007-11-16

Available Online: 2008-04-05

Abstract:

The bipartite entanglement of the two- and three-spin Heisenberg model was investigated by using the concept of negativity. It is found that for the ground-state entanglement of the two-spin model, the negativity always decreases as B increases if Δ<γ－1, and it may keep a steady value of 0.5 in the region of B<J[(Δ+1)²－γ²]^1/2if Δ>γ－1, while for that of the three-spin model, the negativity exhibits square wave structures if γ=0 or Δ=0. For thermal states, there are two areas showing entanglement, namely, the main region and the sub-region. The main region exists only when Δ>Δ_c (Δ_c=γ－1 and (γ²－1)/2 for the 2- and 3-spin model respectively) and extends in terms of B and T as Δ increases, while the sub-region survives only when γ≠0 and shrinks in terms of B and T as Δ increases.

HTML

Reference (1)

Bipartite entanglement in spin-1/2 Heisenberg model

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article