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《中国物理C》（英文）编辑部
2024年10月30日
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

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

  • 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 |Ψa>=|1…1> representing all particles spin up and |Ψb>=|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 |Ψpt>=√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.
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    [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

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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
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Received: 2014-01-10
Revised: 2014-04-15
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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 |Ψa>=|1…1> representing all particles spin up and |Ψb>=|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 |Ψpt>=√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.

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