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Quantum Phase Transitions in Conventional Matrix Product Systems

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Abstract

For matrix product states(MPSs) of one-dimensional spin-\(\frac {1}{2}\) chains, we investigate a new kind of conventional quantum phase transition(QPT). We find that the system has two different ferromagnetic phases; on the line of the two ferromagnetic phases coexisting equally, the system in the thermodynamic limit is in an isolated mediate-coupling state described by a paramagnetic state and is in the same state as the renormalization group fixed point state, the expectation values of the physical quantities are discontinuous, and any two spin blocks of the system have the same geometry quantum discord(GQD) within the range of open interval (0,0.25) and the same classical correlation(CC) within the range of open interval (0,0.75) compared to any phase having no any kind of correlation. We not only realize the control of QPTs but also realize the control of quantum correlation of quantum many-body systems on the critical line by adjusting the environment parameters, which may have potential application in quantum information fields and is helpful to comprehensively and deeply understand the quantum correlation, and the organization and structure of quantum correlation especially for long-range quantum correlation of quantum many-body systems.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grant No.10974137 and the Major Natural Science Foundation of the Educational Department of Sichuan Province under Grant No.14ZA0167.

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Authors and Affiliations

  1. College of Optoelectronics Technology, Chengdu University of Information Technology, Chengdu, 610225, China

    Jing-Min Zhu

  2. College of communication engineering, Chengdu University of Information Technology, Chengdu, 610225, China

    Fei Huang

  3. College of information security engineering, Chengdu University of Information Technology, Chengdu, 610225, China

    Yan Chang

Authors
  1. Jing-Min Zhu
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  2. Fei Huang
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  3. Yan Chang
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Correspondence to Jing-Min Zhu.

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Zhu, JM., Huang, F. & Chang, Y. Quantum Phase Transitions in Conventional Matrix Product Systems. Int J Theor Phys 56, 313–320 (2017). https://doi.org/10.1007/s10773-016-3163-z

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  • DOI: https://doi.org/10.1007/s10773-016-3163-z

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