Quantum phase transitions in matrix product states ofone-dimensional spin-1/2 chains

ZHU Jing-Min

doi:10.1088/1674-1137/38/12/123102

Chinese Physics C> 2014, Vol. 38> Issue(12) : 123102 DOI: 10.1088/1674-1137/38/12/123102

Quantum phase transitions in matrix product states ofone-dimensional spin-1/2 chains

ZHU Jing-Min

College of Optoelectronic Technology, Chengdu University of Information Technology, Chengdu 610225, China

Abstract
HTML
Reference
Related

PDF

Abstract：
For the matrix product system of a one-dimensional spin-1/2 chain, we present a new model of quantum phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively described by phases |Ψ_a>=|1…1> representing all particles spin up and |Ψ_b>=|0…0> representing all particles spin down, while the phase transition point is an isolated intermediate-coupling point where the two phases coexist equally, which is described by the so-called N-qubit maximally entangled GHZ state |Ψ_pt>=√2/2(|1…1>+|0…0>). At the critical point, the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-qubit maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of potential directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-qubit maximal entanglement.

References

[1]

Fannes M, Nachtergaele B, Werner R F. Commun. Math. Phys., 1992, 144: 443[2] Verstraete F, Porras D, Cirac J I. Phys. Rev. Lett., 2004, 93: 227205[3] Verstraete F, Cirac J I. arXiv: cond-mat/0505140; Osborne T J. arXiv: quant-ph/0508031; Hastings M B. arXiv: cond-mat/0508554[4] Garcia D P, Verstraete F, Wolf M M, Cirac J I. Quantum Inf. Comput., 2007, 7: 401[5] Affleck I, Kennedy T, Lieb E H, Tasaki H. Commun. Math. Phys., 1988, 115: 477[6] Klümper A, Schadschneider A, Zittartz J. J. Phys. A, 1991, 24: L955; Z. Phys. B, 1992, 87: 281[7] Klümper A, Schadschneider A, Zittartz J. Europhys. Lett., 1993, 24: 293[8] Wolf M M, Ortiz G, Verstraete F et al. Phys. Rev. Lett., 2006, 97: 110403[9] Asoudeh M, Karimipour V, Sadrolashrafi L A. Phys. Rev. B, 2007, 75: 224427[10] Alipour S, Karimipour V, Memarzadeh L. Phys. Rev. A, 2007, 75: 052322[11] ZHU Jing-Min. Chin. Phys. Lett., 2008, 25(10):3574-3577[12] ZHU Jing-Min. Chinese Physics C (HEP NP), 2011, 35(02): 144-148[13] ZHU Jing-Min. Chin. Phys. C, 2014, 38(10): 103102[14] Nielsen N, Chuang I. Quantum Computation and Quantum Communication. Cambridge: Cambridge University Press, 2000[15] QIN M, TAO Y J. Chinese Physics C(HEP NP), 2008, 32(09): 710-713[16] ZHU Jing-Min, WANG S J. Commun. Theor. Phys., 2010, 54(3): 524-528[17] LIU W Z, ZHANG J F, LONG G L. Chinese Science Bulletin, 2009, 54: 4262-4265[18] WEN Wei. Science China Physics, Mechanics and Astronomy, 2013, 56(5): 947-951[19] ZHAO Hui, ZHANG Xing-Hua, FEI Shao-Ming et al. Chinese Science Bulletin, 2013, 58(19): 2334-2339[20] MAN Zhong-Xiao, SU Fang, XIA Yun-Jie. Chinese Science Bulletin, 2013, 58(20): 2423-2429[21] MA Xiao-San, QIAO Ying, ZHAO Guang-Xing et al. Science China Physics, Mechanics and Astronomy, 2013, 56(3): 600-605[22] CAO Ye, LI Hui, LONG Gui-Lu. Chinese Science Bulletin, 2013, 58(1): 48-52[23] CAO Wan-Cang, LIU Dan, PAN Feng et al. Science in China Series G-Physics Mechanics Astron, 2006, 49(5): 606[24] LIU Dan, ZHAO Xin, LONG Gui-Lu. Commun. Theor. Phys., 2010, 54: 825-828 (or arXiv: quant-ph/07053904)[25] LIU Dan, ZHAO Xin, LONG Gui-Lu. Commun. Theor. Phys., 2008, 49: 329[26] WU Hua, ZHAO Xin, LI Yan-Song et al. International Journal Of Quantum Information, 2010, 8(7): 1169-1177[27] Muralidharan S, Panigrahi P K. Phy. Rev. A, 2008, 77: 032321[28] Muralidharan S, Panigrahi P K. Phy. Rev. A, 2008, 78: 062333[29] ZHU Jing-Min. Commun. Theor. Phys., 2010, 54(2): 373-379[30] ZHU Jing-Min. Chinese Physics C (HEP NP), 2012, 36(4): 311-315[31] Nachtergaele B. Commun. Math. Phys., 1996, 175: 565[32] Verstraete F, Cirac J I, Latorre J I, Rico E, Wolf M M. Phys. Rev. Lett., 2005, 94: 140601

[1]	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
[2]	QIN Zhen-Xing , TANG Ling-Yun , LIU Jing , CHEN Xiao-Jia . Phase transitions in a hydrogen-rich compound：tetramethylsilane. Chinese Physics C, 2013, 37(9): 098001. doi: 10.1088/1674-1137/37/9/098001
[3]	PAN Xue , CHEN Li-Zhu , CHEN Xiao-Song , WU Yuan-Fang . Cumulants in the 3-dimensional Ising, O(2) and O(4) spin models. Chinese Physics C, 2013, 37(12): 124103. doi: 10.1088/1674-1137/37/12/124103
[4]	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
[5]	CHEN Liang , ZHOU Xiao-Hong , ZHANG Yu-Hu , LIU Min-Liang , WANG Shi-Tao , FANG Yong-De , HUA Wei , QIANG Yun-Hua , LI Guang-Shun , ZHOU Hou-Bing , DING Bing , WANG Hai-Xia , ZHENG Yong , ZHU Li-Hua , WU Xiao-Guang . Reinvestigation of the high spin states in ¹⁶¹Er and enhanced E1 transitions in the N=93 isotones. Chinese Physics C, 2011, 35(6): 545-549. doi: 10.1088/1674-1137/35/6/007
[6]	ZHU Jing-Min . Quantum phase transitions about parity breaking in matrix product systems. Chinese Physics C, 2011, 35(2): 144-148. doi: 10.1088/1674-1137/35/2/007
[7]	. 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
[8]	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
[9]	HU Ming-Liang , TIAN Dong-Ping . Bipartite entanglement in spin-1/2 Heisenberg model. Chinese Physics C, 2008, 32(4): 303-307. doi: 10.1088/1674-1137/32/4/013
[10]	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.
[11]	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.
[12]	Chen Qizhou , Fang Xiyan , Guo Shouhong . Calculation of Vacuum State for 2+1-Dimensional SU(3) Lattice Gauge Theory. Chinese Physics C, 1995, 19(S3): 265-272.
[13]	Gao Xiaochun , Xu Donghui . Removability of the Topological Term in the 2+1 Dimensional CP¹ Model. Chinese Physics C, 1995, 19(S3): 257-264.
[14]	SHEN Kun , QIU Zhong-Ping . Vertex Correction and Phase Structure in (2+1) Dimensional Chiral Gross-Neveu Model. Chinese Physics C, 1993, 17(9): 811-815.
[15]	Shen Kun , Qiu Zhongping . Vertex Correction at Finite Temperature and Decoupling Phase Transition in 2+1-Dimensional Chiral Gross-Neveu Model. Chinese Physics C, 1993, 17(S3): 261-270.
[16]	Li Xianyin , Zhao Xiaofeng . A Microscopic IBM-2 Description of the Phase Transitions of Nuclear Spectrum Structure Near A=130. Chinese Physics C, 1991, 15(S2): 183-188.
[17]	Li Zhibing , Zheng Weihong , Guo Shuohong . The String Tensions of (2+1)-dimensional SU(2) Gauge Theory. Chinese Physics C, 1989, 13(S3): 245-248.
[18]	Zheng Weihong , Guo Shuohong . Variational Calculation of the Glueball Mass in 2+1 Dimensional SU(2) LGT. Chinese Physics C, 1989, 13(S1): 33-36.
[19]	Liu Jinming , Zheng Weihong , Guo Shuohong . The Mass Gap in 2 + 1 Dimensional SU(3) Lattice Gauge Theory. Chinese Physics C, 1988, 12(S2): 137-142.
[20]	Zheng Weihong , Liu Jinming , Guo Shuohong . The Mass Gap in 2 + 1 Dimensional SU(2) Lattice Gauge Theory. Chinese Physics C, 1988, 12(S1): 51-54.

Access

Get Citation

ZHU Jing-Min. Quantum phase transitions in matrix product states ofone-dimensional spin-1/2 chains[J]. Chinese Physics C, 2014, 38(12): 123102. doi: 10.1088/1674-1137/38/12/123102

ZHU Jing-Min. Quantum phase transitions in matrix product states ofone-dimensional spin-1/2 chains[J]. Chinese Physics C, 2014, 38(12): 123102. doi: 10.1088/1674-1137/38/12/123102 shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2014-01-10
Revised: 2014-04-15

Article Metric

Article Views(1888)
PDF Downloads(183)
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

Quantum phase transitions in matrix product states ofone-dimensional spin-1/2 chains

College of Optoelectronic Technology, Chengdu University of Information Technology, Chengdu 610225, China

Received Date: 2014-01-10

Accepted Date: 2014-04-15

Available Online: 2014-12-05

Abstract: For the matrix product system of a one-dimensional spin-1/2 chain, we present a new model of quantum phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively described by phases |Ψ_a>=|1…1> representing all particles spin up and |Ψ_b>=|0…0> representing all particles spin down, while the phase transition point is an isolated intermediate-coupling point where the two phases coexist equally, which is described by the so-called N-qubit maximally entangled GHZ state |Ψ_pt>=√2/2(|1…1>+|0…0>). At the critical point, the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-qubit maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of potential directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-qubit maximal entanglement.

HTML

Reference (1)

Quantum phase transitions in matrix product states ofone-dimensional spin-1/2 chains

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article

Quantum phase transitions in matrix product states ofone-dimensional spin-1/2 chains

HTML

目录