Quantum phase transitions in matrix product states of one-dimensional spin-1 chains

  • We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equal coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-spin 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 certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-spin maximal entanglement.
      PCAS:
  • 加载中
  • [1] Sachdev S. Quantum Phase Transitions. Cambridge: Cambridge University Press, 1999[2] Fannes M, Nachtergaele B, Werner R F. Commun. Math. Phys., 1992, 144: 443[3] Verstraete F, Porras D, Cirac J I. Phys. Rev. Lett., 2004, 93: 227205[4] Verstraete F, Cirac J I. arXiv: cond-mat/0505140; Osborne T J. arXiv: quant-ph/0508031; Hastings M B. arXiv: cond-mat/0508554[5] Garcia D P, Verstraete F, Wolf M M, Cirac J I. Quantum Inf. Comput., 2007, 7: 401[6] Affleck I, Kennedy T, Lieb E H, Tasaki H. Commun. Math. Phys., 1988, 115: 477[7] Klümper A, Schadschneider A, Zittartz J. J. Phys. A, 1991, 24, L955; Z. Phys. B, 1992, 87: 281[8] Klümper A, Schadschneider A, Zittartz J., Europhys. Lett., 1993, 24: 293[9] Wolf M M, Ortiz G, Verstraete F et al. Phys. Rev. Lett., 2006, 97: 110403[10] Asoudeh M, Karimipour V, Sadrolashrafi L A. Phys. Rev. B, 2007, 75: 224427[11] Alipour S, Karimipour V, Memarzadeh L. Phys. Rev. A, 2007, 75: 052322[12] Nielsen N, Chuang I. Quantum Computation and Quantum Communication. Cambridge: Cambridge University Press, 2000[13] QIN M, TAO Y J. Chinese Physics C (HEP NP), 2008, 32(09): 710-713[14] ZHU Jing-Min, WANG S J. Commun. Theor. Phys., 2010, 54(3): 524-528[15] LIU W Z, ZHANG J F, LONG G L. Chinese Science Bulletin, 2009, 54: 4262-4265[16] WEN Wei. Science China Physics, Mechanics and Astronomy, 2013, 56(5): 947-951[17] ZHAO Hui, ZHANG Xing-Hua, FEI Shao-Ming et al. Chinese Science Bulletin, 2013, 58(19): 2334-2339[18] MAN Zhong-Xiao, SU Fang, XIA Yun-Jie. Chinese Science Bulletin, 2013, 58(20): 2423-2429[19] MA Xiao-San, QIAO Ying, ZHAO Guang-Xing et al. Science China Physics, Mechanics and Astronomy, 2013, 56(3): 600-605[20] CAO Ye, LI Hui, LONG Gui-Lu. Chinese Science Bulletin, 2013, 58(1): 48-52[21] CAO Wan-Cang, LIU Dan, PAN Feng et al. Science in China Series G-Physics Mechanics Astron, 2006, 49(5): 606[22] LIU Dan, ZHAO Xin, LONG Gui-Lu. Commun. Theor. Phys., 2010, 54: 825-828 (or arXiv: quant-ph/07053904)[23] LIU Dan, ZHAO Xin, LONG Gui-Lu. Commun. Theor. Phys., 2008, 49: 329[24] WU Hua, ZHAO Xin, LI Yan-Song et al. International Journal of Quantum Information, 2010, 8(7): 1169-1177[25] Muralidharan S, Panigrahi P K. Phy. Rev. A, 2008, 77: 032321[26] Muralidharan S, Panigrahi P K. Phy. Rev. A, 2008, 78: 062333[27] ZHU Jing-Min. Commun. Theor. Phys., 2010, 54(2): 373-379[28] ZHU Jing-Min. Chinese Physics C, 2012, 36(4): 311-315[29] Nachtergaele B. Commun. Math. Phys., 1996, 175: 565[30] Verstraete F, Cirac J I, Latorre J I, Rico E, Wolf M M. Phys. Rev. Lett., 2005, 94: 140601
  • 加载中

Get Citation
ZHU Jing-Min. Quantum phase transitions in matrix product states of one-dimensional spin-1 chains[J]. Chinese Physics C, 2014, 38(10): 103102. doi: 10.1088/1674-1137/38/10/103102
ZHU Jing-Min. Quantum phase transitions in matrix product states of one-dimensional spin-1 chains[J]. Chinese Physics C, 2014, 38(10): 103102.  doi: 10.1088/1674-1137/38/10/103102 shu
Milestone
Received: 2013-12-18
Revised: 2014-01-07
Article Metric

Article Views(1170)
PDF Downloads(182)
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

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Email This Article

Title:
Email:

Quantum phase transitions in matrix product states of one-dimensional spin-1 chains

    Corresponding author: ZHU Jing-Min,
  • College of Optoelectronic Technology, Chengdu University of Information Technology, Chengdu 610225, China

Abstract: We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equal coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-spin 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 certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-spin maximal entanglement.

    HTML

Reference (1)

目录

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return