Quantum fidelity, string order parameter, and topological quantum phase transition in a spin-1/2 dimerized and frustrated Heisenberg chain

Regular Article

Abstract

Topological quantum phase transitions are numerically investigated in a spin-1/2 dimerized and frustrated Heisenberg chain by using infinite matrix product state representation with the infinite time evolving block decimation method. Quantum fidelity approach is employed to detect the degenerate ground states and quantum phase transitions. By calculating the long-range string order parameters, we find two topological Haldane phases characterized by two long-range string orders. Also, continuous and discontinuous behaviors of von Neumann entropy show that phase transitions between two topological Haldane phases are topologically continuous and discontinuous quantum phase transitions. For the topologically continuous phase transition, the central charge at the critical point is obtained as c = 1, which means that the topologically continuous quantum phase transition belongs to the Gaussian universality class.

Keywords

Solid State and Materials 

References

  1. 1.
    F. Verstraete, M.A. Martin-Delgado, J.I. Cirac, Phys. Rev. Lett. 92, 087201 (2004) CrossRefADSGoogle Scholar
  2. 2.
    L. Amico, F. Baroni, A. Fubini, D. Patan’e, V. Tognetti, P. Verrucchi, Phys. Rev. A 74, 022322 (2006) CrossRefADSGoogle Scholar
  3. 3.
    G. Vidal, J.I. Latorre, E. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003) CrossRefADSGoogle Scholar
  4. 4.
    P. Calabrese, J. Cardy, J. Stat. Mech. 0406, 06002 (2004) CrossRefGoogle Scholar
  5. 5.
    H.L. Haselgrove, M.A. Nielsen, T.J. Osborne, Phys. Rev. A 69, 032303 (2004) MathSciNetCrossRefADSGoogle Scholar
  6. 6.
    H.-Q. Zhou, J.-H. Zhao, B. Li, Phys. Rev. E 41, 492002 (2008) MathSciNetGoogle Scholar
  7. 7.
    J.-H. Zhao, H.-L. Wang, B. Li, H.-Q. Zhou, Phys. Rev. E 82, 061127 (2010) CrossRefADSGoogle Scholar
  8. 8.
    Y.H. Su, B.-Q. Hu, S.-H. Li, S.Y. Cho, Phys. Rev. E 88, 032110 (2013) CrossRefADSGoogle Scholar
  9. 9.
    Y.-W. Dai, S.Y. Cho, Murray T. Batchelor, H.-Q. Zhou, Phys. Rev. E 89, 032110 (2014) CrossRefGoogle Scholar
  10. 10.
    P.W. Anderson, Basic Notions of Condensed Matter Physics (Addison-Wesley, Reading, 1997)Google Scholar
  11. 11.
    S. Coleman, in An Introduction to Spontaneous Symmetry Breakdown and gauge Fields, Laws of Hadronic Matter, edited by A. Zichichi (Academic, New York, 1975)Google Scholar
  12. 12.
    M. den Nijs, K. Rommelse, Phys. Rev. B 40, 4709 (1989) CrossRefADSGoogle Scholar
  13. 13.
    X.-Y. Feng, G.-M. Zhang, T. Xiang, Phys. Rev. Lett. 98, 087204 (2007) CrossRefADSGoogle Scholar
  14. 14.
    H.D. Chen, Z. Nussinov, J. Phys. A 41, 075001 (2008) MathSciNetCrossRefADSGoogle Scholar
  15. 15.
    F.C. Alcaraz, Y. Hatsugai, Phys. Rev. B 46, 13914 (1992) CrossRefADSGoogle Scholar
  16. 16.
    A.K. Kolezhuk, U. Schollwöck, Phys. Rev. B 65, 100401 (2002) CrossRefADSGoogle Scholar
  17. 17.
    K. Hida, Phys. Rev. B 45, 2207 (1992) MathSciNetCrossRefADSGoogle Scholar
  18. 18.
    H.-H. Hung, C.-D. Gong, Phys. Rev. B 71, 13914 (2005) CrossRefGoogle Scholar
  19. 19.
    S. Yamamoto, Phys. Rev. B 55, 3603 (1997) CrossRefADSGoogle Scholar
  20. 20.
    Y.H. Su, S.Y. Cho, B. Li, H.L. Wang, H.-Q. Zhou, J. Phys. Soc. Jpn 81, 074003 (2012) CrossRefADSGoogle Scholar
  21. 21.
    D.G. Shelton, A.A. Nersesyan, A.M. Ysvelik, Phys. Rev. B 53, 8521 (1996) CrossRefADSGoogle Scholar
  22. 22.
    H. Tasaki, Phys. Rev. Lett. 66, 798 (1991)MATHMathSciNetCrossRefADSGoogle Scholar
  23. 23.
    H. Watanabe, K. Nomura, S. Takada, J. Phys. Soc. Jpn 62, 2845 (1993) CrossRefADSGoogle Scholar
  24. 24.
    Y. Nishiyama, N. Hatano, M. Suzuki, J. Phys. Soc. Jpn 64, 1967 (1995) CrossRefADSGoogle Scholar
  25. 25.
    S.R. White, Phys. Rev. B 53, 52 (1996)CrossRefADSGoogle Scholar
  26. 26.
    E.H. Kim, G. Fáth, J. Slyom, D.J. Scalapino, Phys. Rev. B 62, 14965 (2000) CrossRefADSGoogle Scholar
  27. 27.
    G. Fáth, Ö. Legeza, J. Sólyom, Phys. Rev. B 63, 134403 (2001) CrossRefADSGoogle Scholar
  28. 28.
    M. Nakamura, S. Todo, Phys. Rev. Lett. 89, 077204 (2002) CrossRefADSGoogle Scholar
  29. 29.
    H.-H. Hung, C.D. Gong, Y.-C. Chen, M.-F. Yang, Phys. Rev. B 73, 224433 (2006) CrossRefADSGoogle Scholar
  30. 30.
    F. Anfuso, A. Rosch, Phys. Rev. B 76, 085124 (2007) CrossRefADSGoogle Scholar
  31. 31.
    E.H. Kim, Ö. Legeza, J. Sólyom, Phys. Rev. B 77, 205121 (2008) CrossRefADSGoogle Scholar
  32. 32.
    V.O. Garlea, A. Zheludev, L.P. Regnault, J.H. Chung, Y. Qiu, M. Boehm, K. Habicht, M. Meissner, Phys. Rev. Lett. 100, 037206 (2008) CrossRefADSGoogle Scholar
  33. 33.
    G. Vidal, Phys. Rev. Lett. 98, 070201 (2007) MathSciNetCrossRefADSGoogle Scholar
  34. 34.
    G. Vidal, Phys. Rev. Lett. 91, 147902 (2003) CrossRefADSGoogle Scholar
  35. 35.
    H.-L. Wang, A.-M. Chen, B. Li, H.-Q. Zhou, J. Phys. A 45, 015306 (2012) MathSciNetCrossRefADSGoogle Scholar
  36. 36.
    R. Chitra, S. Pati, H.R. Krishnamurthy, D. Sen, S. Ramasesha, Phys. Rev. B 52, 6581 (1995) CrossRefADSGoogle Scholar
  37. 37.
    V.M.L. Durga Prasad, S. Sahoo, S. Ramasesha, D. Sen, J. Phys.: Condens. Matter 25, 125603 (2013) ADSGoogle Scholar
  38. 38.
    S. Shastry, B. Sutherland, Phys. Rev. Lett. 47, 964 (1981)CrossRefADSGoogle Scholar
  39. 39.
    C.K. Majumdar, D.K. Ghosh, J. Math. Phys. 10, 1388 (1969) MathSciNetCrossRefADSGoogle Scholar
  40. 40.
    Hai Tao Wang, Bo Li, Sam Young Cho, Phys. Rev. B 87, 054402 (2013) CrossRefADSGoogle Scholar
  41. 41.
    T. Tonegawa, I. Harada, J. Math. Phys. 56, 2153 (1987) Google Scholar
  42. 42.
    K, Okamoto, K. Nomura. Phys. Lett. A 169, 433 (1992)CrossRefADSGoogle Scholar
  43. 43.
    S. Eggert, Phys. Rev. B 54, R9612 (1996) CrossRefADSGoogle Scholar
  44. 44.
    T. Kennedy, H. Tasaki, Phys. Rev. B 45, 304 (1992)CrossRefADSGoogle Scholar
  45. 45.
    P. Calabrese, J. Cardy, J. Phys. A 42, 504005 (2009) MathSciNetCrossRefGoogle Scholar
  46. 46.
    J. Cardy, Scaling and Renormalization in Statistical Physics (University of Oxford, Oxford, 1996)Google Scholar
  47. 47.
    L. Tagliacozzo, T.R. de Oliveira, S. Iblisdir, J.I. Latorre, Phys. Rev. B 78, 024410 (2008) CrossRefADSGoogle Scholar
  48. 48.
    F. Pollmann, S. Mukerjee, A. Turner, J.E. Moore, Phys. Rev. Lett. 102, 255701 (2009) CrossRefADSGoogle Scholar
  49. 49.
    G. Vidal, J.I. Latorre, E. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003) CrossRefADSGoogle Scholar
  50. 50.
    C.H. Bennett, H.J. Bernstein, S. Popescu, B. Schumacher, Phys. Rev. A 53, 2046 (1996)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Physics and Electronic Science, Guizhou Normal UniversityGuiyangP.R. China
  2. 2.College of Materials and Engineering, Chongqing UniversityChongqingP.R. China

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