Effects of the Next-Nearest-Neighbor Interaction on the Entanglement of the Heisenberg XX Chain

HU Ming-Liang; TIAN Dong-Ping

Chinese Physics C> 2006, Vol. 30> Issue(11) : 1132-1136

Effects of the Next-Nearest-Neighbor Interaction on the Entanglement of the Heisenberg XX Chain

HU Ming-Liang ^, ,
TIAN Dong-Ping

School of Science, Xi'an Jiaotong University, Xi'an 710049, China2 Xi'an Institute of Post and Telecommunication, Xi'an 710061,China

Abstract
HTML
Reference
Related

PDF

Abstract：
The pairwise entanglement of the Heisenberg XX chain with next-nearest-neighbor (NNN) interactions was investigated by using the concurrence measure. The results show that for the nearest-neighbor sites, the entanglement may be improved or suppressed depending on the magnitudes of the NNN coupling constant J, while for the next-nearest-neighbor sites, it always increases with the increase of |J|. The critical temperature T_c decreases with the increase of J for the nearest-neighbor entanglement and increases with the increase of |J| for the next-nearest-neighbor entanglement, respectively. We also show that the general Heisenberg XX model still can be used to create the entangled W states of three and four qubits, and that the presence of NNN coupling has no effect on the creation of four-qubit W states, while it shifts the instant of time at which the three-qubit W states are created.

References

[1]

. Bennett C H, Brassard G, Crépeau C et al. Phys. Rev.Lett., 1993, 70(13): 1895-18992. Ekert A K. Phys. Rev. Lett., 1991, 67(6): 661-6633. DiVincenzo D P, Eacon D, Kempe J et al. Nature, 2000,408(6810): 339-3424. Bennett C H, Wiesner S J. Phys. Rev. Lett., 1992, 69(20):2881-28845. WANG X G. Phys. Rev., 2001, A64(1): 0123136. CAO M, ZHU S Q. Phys. Rev., 2005, A71: 0343117. Kamta G L, Starace A F. Phys. Rev. Lett., 2002, 88(10):1079018. Arnesen M C, Bose S, Vedral V. Phys. Rev. Lett.,2001,87(1): 0179019. Asoudeh M, Karimipour V. Phys. Rev., 2005, A71: 02230810. ZHANG G F, LI S S. Phys. Rev., 2005, A72: 03430211. ZHOU L, SONG H S, GUO Y Q et al. Phys. Rev., 2003,A68: 02430112. HU M L, TIAN D P. J. At. Mol. Phys., Accepted13. GU S J, LI H B, LI Y Q et al. Phys. Rev., 2004, A70:05230214. Bose I. E-print, cond-mat/010739915. Hill S, Wootters W K. Phys. Rev. Lett., 1997, 78(26):5022-502516. Wootters W K. Phys. Rev. Lett., 1998, 80(10): 2245-2248

[1]	TIAN Dong-Ping , HU Ming-Liang . Dynamics of Multipartite Entanglement in the Heisenberg Model. Chinese Physics C, 2007, 31(5): 509-512.
[2]	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.
[3]	ZHANG Yin-Jie , SHEN Peng-Nian , ZOU Bing-Song . Study of KK strong interaction bound state and K⁺K^－ atomic state. Chinese Physics C, 2006, 30(3): 212-216.
[4]	LIU Xi-Ming . Test of Flavor Independence in Strong Interaction. Chinese Physics C, 2004, 28(10): 1026-1032.
[5]	JIN Da-Peng , LU Feng , GUO Ya-Nan , WANG Yi-Fang , WU Ling-Hui , LIU Zhen-An , YU Zhong-Qiang . Monte Carlo Simulation of the BEPCⅡ/BESⅢ Backgrounds—Beam-Gas Interactions. Chinese Physics C, 2004, 28(11): 1197-1202.
[6]	ZHANG Miao-Jing , SHEN Peng-Nian , LIU Xian-Hui , KONG Fan-Xin . Study about Light Hypernuclei and YN Interaction Based on Chiral SU(3) Quark Model. Chinese Physics C, 2001, 25(8): 743-753.
[7]	Zhang Qingying , Fu Liping . Study of Spectra with Boson ConfigurationMixing and Surface Delta Interaction. Chinese Physics C, 1998, 22(3): 260-264.
[8]	Wang Renchuan , Zhu Dongpei . On the Quantization of Interacting Fields in QED. Chinese Physics C, 1994, 18(11): 1012-1019.
[9]	SHEN Xiao-Yan , SHEN Peng-Nian , YU You-Wen , ZHANG Zong-Ye . Color Screening Effect and N-N Scattering. Chinese Physics C, 1993, 17(9): 816-821.
[10]	SUN Chang-Pu , PAN Lin , GE Mo-Lin . Effective topological action in Heisenberg spin model as Berry's phase. Chinese Physics C, 1992, 16(3): 202-207.
[11]	CUI Huan-Hua , KE Wei , ZHOU Jian , LV Wei-Chun . STUDY ON THE INTERACTION OF 960A MeV ²³⁸U IONS WITH LIGHT NUCLEI. Chinese Physics C, 1989, 13(3): 199-204.
[12]	GU Ying-Qi , MA Zhong-Yu , ZHUO Yi-Zhong . QUARK SELF-ENERGY DUE TO QUARK-PION INTERACTION. Chinese Physics C, 1987, 11(3): 362-368.
[13]	JIANG Guo-Rong , JIN Xing-Nan . THE Λ-α EFFECTIVE INTERACTION AND INVESTIGATION ON THE HYPERNUCLEI ⁶_ΛΛHe AND ⁹_ΛBe. Chinese Physics C, 1987, 11(2): 226-230.
[14]	WANG Zheng-Da . A STUDY OF THE NUCLEAR POTENTIAL BETWEEN TWO NUCLEI. Chinese Physics C, 1986, 10(3): 349-353.
[15]	HU Bing-Quan , HE Qi-Zhi , ZHANG Zhao-Xi , AN Ying . THE EFFECTIVE INTERMEDIATE RANGE INTERACTION IN BARYON SPECTROSCOPY AND ITS EFFECT ON N-N INTERATION. Chinese Physics C, 1986, 10(6): 677-683.
[16]	CHENG Tan-Sheng , ZHONG Yu-Shu , XU Zhan . LONG RANGE POTENTIAL BETWEEN NUCLEONS. Chinese Physics C, 1984, 8(1): 91-98.
[17]	WANG XIU-JIANG , FAN JI . THE MESON EXCHANGE POTENTIALS OF THE Σ-N INTERACTION. Chinese Physics C, 1983, 7(6): 709-715.
[18]	SHI YI-JIN , ZHUANG FEI . SYSTEMATIC STUDY ON 1-p SHELL HYPERNUCLEI(Ⅰ)——Λ-N EFFECTIVE INTERACTION. Chinese Physics C, 1982, 6(6): 750-759.
[19]	GUO HAN-YING . THE INDUCED KALUZA TYPE INTERACTIONS. Chinese Physics C, 1982, 6(2): 247-250.
[20]	YU YOU-WEN . THE INTERACTION OF ANTINUCLEON WITH NUCLEUS. Chinese Physics C, 1979, 3(6): 676-680.

Access

Get Citation

HU Ming-Liang and TIAN Dong-Ping. Effects of the Next-Nearest-Neighbor Interaction on the Entanglement of the Heisenberg XX Chain[J]. Chinese Physics C, 2006, 30(11): 1132-1136.

HU Ming-Liang and TIAN Dong-Ping. Effects of the Next-Nearest-Neighbor Interaction on the Entanglement of the Heisenberg XX Chain[J]. Chinese Physics C, 2006, 30(11): 1132-1136. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2006-03-07
Revised: 2006-05-22

Article Metric

Article Views(3533)
PDF Downloads(763)
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

Effects of the Next-Nearest-Neighbor Interaction on the Entanglement of the Heisenberg XX Chain

HU Ming-Liang ^,
TIAN Dong-Ping

Corresponding author: HU Ming-Liang,

School of Science, Xi'an Jiaotong University, Xi'an 710049, China2 Xi'an Institute of Post and Telecommunication, Xi'an 710061,China

Received Date: 2006-03-07
Accepted Date: 2006-05-22
Available Online: 2006-11-05

Abstract: The pairwise entanglement of the Heisenberg XX chain with next-nearest-neighbor (NNN) interactions was investigated by using the concurrence measure. The results show that for the nearest-neighbor sites, the entanglement may be improved or suppressed depending on the magnitudes of the NNN coupling constant J, while for the next-nearest-neighbor sites, it always increases with the increase of |J|. The critical temperature T_c decreases with the increase of J for the nearest-neighbor entanglement and increases with the increase of |J| for the next-nearest-neighbor entanglement, respectively. We also show that the general Heisenberg XX model still can be used to create the entangled W states of three and four qubits, and that the presence of NNN coupling has no effect on the creation of four-qubit W states, while it shifts the instant of time at which the three-qubit W states are created.