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Journal of the Korean Physical Society

, Volume 68, Issue 9, pp 1114–1119 | Cite as

The antiferromagnetic cross-coupled spin ladder: Quantum fidelity and tensor networks approach

  • Xi-Hao Chen
  • Sam Young ChoEmail author
  • Huan-Qiang Zhou
  • Murray T. Batchelor
Article

Abstract

We investigate the phase diagram of the cross-coupled Heisenberg spin ladder with antiferromagnetic couplings. For this model, the results for the existence of the columnar dimer phase, which was predicted on the basis of weak coupling field theory renormalization group arguments, have been conflicting. The numerical work on this model has been based on various approaches, including exact diagonalization, series expansions and density-matrix renormalization group calculations. Using the recently-developed tensor network states and groundstate fidelity approach for quantum spin ladders, we find no evidence for the existence of the columnar dimer phase. We also provide an argument based on the symmetry of the Hamiltonian, which suggests that the phase diagram for antiferromagnetic couplings consists of a single line separating the rung-singlet and the Haldane phases.

Keywords

Spin ladder Quantum phase transition Tensor networks Fidelity 

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References

  1. [1]
    See, e.g., reviews on various aspects in Frustrated Spin Systems, edited by H. T. Diep (World Scientific, Singapore, 2005); Quantum Magnetism, edited by U. Schollwöck, J. Richter, D. J. J. Farnell and R. F. Bishop, Lect. Notes Phys. 645 (Springer, Berlin, 2004).Google Scholar
  2. [2]
    For reviews, see, e.g., E. M. Dagotto and T. M. Rice, Science 271, 618 (1996)Google Scholar
  3. [2a]
    E. Dagotto, Rep. Prog. Phys. 62, 1525 (1999)CrossRefADSGoogle Scholar
  4. [2b]
    M. T. Batchelor, X.-W. Guan, N. Oelkers and Z. Tsuboi, Adv. Phys. 56, 465 (2007).CrossRefADSGoogle Scholar
  5. [3]
    M. P. Gelfand, Phys. Rev. B 43, 8644 (1991).CrossRefADSGoogle Scholar
  6. [4]
    I. Bose and S. Gayen, Phys. Rev. B 48, 10653 (1993).CrossRefADSGoogle Scholar
  7. [5]
    Y. Xian, Phys. Rev. B 52, 12485 (1995).CrossRefADSGoogle Scholar
  8. [6]
    H. Kitatani and T. Oguchi, J. Phys. Soc. Jpn. 65, 1387 (1996).CrossRefADSGoogle Scholar
  9. [7]
    W. H. Zheng, V. Kotov and J. Oitmaa, Phys. Rev. B 57, 11439 (1998).CrossRefADSGoogle Scholar
  10. [8]
    A. K. Kolezhuk and H.-J. Mikeska, Int. J. Mod. Phys. B 05, 2325 (1998).MathSciNetCrossRefADSGoogle Scholar
  11. [9]
    D. Allen, F. H. L. Essler and A. A. Nersesyan, Phys. Rev. B 61, 8871 (2000).CrossRefADSGoogle Scholar
  12. [10]
    E. H. Kim, G. Fáth, J. Sólyom and D. J. Scalapino, Phys. Rev. B 62, 14965 (2000).CrossRefADSGoogle Scholar
  13. [11]
    A. Honecker, F. Mila and M. Troyer, Eur. Phys. J. B 15, 227 (2000).CrossRefADSGoogle Scholar
  14. [12]
    X. Q. Wang, Mod. Phys. Lett. B 14, 327 (2000).CrossRefADSGoogle Scholar
  15. [13]
    G. Fáth, Ö. Ligeza and J. Sólyom, Phys. Rev. B 63, 134403 (2001).CrossRefADSGoogle Scholar
  16. [14]
    T. Hakobyan, J. H. Hetherington and M. Roger, Phys. Rev. B 63, 144433 (2001).CrossRefADSGoogle Scholar
  17. [15]
    A. A. Nersesyan and A. M. Tsvelik, Phys. Rev. B 67, 024422 (2003).CrossRefADSGoogle Scholar
  18. [16]
    M. Nakamura and S. Todo, Prog. Theor. Phys. Suppl. 145, 217 (2002).CrossRefADSGoogle Scholar
  19. [17]
    M. Nakamura, Physica B 329-333, 1000 (2003).CrossRefADSGoogle Scholar
  20. [18]
    O. A. Starykh and L. Balents, Phys. Rev. Lett. 93, 127202 (2004).CrossRefADSGoogle Scholar
  21. [19]
    H.-H. Hung, C.-D. Gong, Y.-C. Chen and M.-F. Yang, Phys. Rev. B 73, 224433 (2006).CrossRefADSGoogle Scholar
  22. [20]
    M. Azzouz and B. W. Ramakko, Can. J. Phys. 86, 509 (2008).CrossRefADSGoogle Scholar
  23. [21]
    E. H. Kim, Ö. Legeza and J. Sólyom, Phys. Rev. B 77, 205121 (2008).CrossRefADSGoogle Scholar
  24. [22]
    G.-H. Liu, H.-L. Wang and G.-S. Tian, Phys. Rev. B 77, 214418 (2008).CrossRefADSGoogle Scholar
  25. [23]
    T. Hikihara and O. A. Starykh, Phys. Rev. B 81, 064432 (2010).CrossRefADSGoogle Scholar
  26. [24]
    S.-H. Li, Q.-Q. Shi, Y.-H. Su, J.-H. Liu, Y.-W. Dai and H.-Q. Zhou, Phys. Rev. B 86, 064401 (2012).CrossRefADSGoogle Scholar
  27. [25]
    G. Barcza, Ö. Legeza, R. M. Noack and J. Sólyom, Phys. Rev. B 86, 075133 (2012).CrossRefADSGoogle Scholar
  28. [26]
    G.-H. Liu, X.-Y. Deng and R. Wen, Physica B 407, 2068 (2012).CrossRefADSGoogle Scholar
  29. [27]
    For a recent review, see R. Orús, Annals of Physics 349, 117 (2014).Google Scholar
  30. [28]
    H.-Q. Zhou and J. P. Barjaktarevic, J. Phys. A 41, 412001 (2008).MathSciNetCrossRefGoogle Scholar
  31. [29]
    H.-Q. Zhou, J.-H. Zhao and B. Li, J. Phys. A 41, 492002 (2008).MathSciNetCrossRefGoogle Scholar
  32. [30]
    J.-H. Zhao, H.-L. Wang, B. Li and H.-Q. Zhou, Phys. Rev. E 82, 061127 (2010).CrossRefADSGoogle Scholar
  33. [31]
    H.-Q. Zhou, R. Orús and G. Vidal, Phys. Rev. Lett. 100, 080601 (2008).CrossRefADSGoogle Scholar
  34. [32]
    Y.-H. Su, B.-Q. Hu, S.-H. Li and S. Y. Cho, Phys. Rev. E 88, 032110 (2013).CrossRefADSGoogle Scholar
  35. [33]
    Y.-W. Dai, S. Y. Cho, M. T. Batchelor and H.-Q. Zhou, Phys. Rev. E 89, 062142 (2014).CrossRefADSGoogle Scholar
  36. [34]
    H.-T. Wang, S. Y. Cho and M. T. Batchelor, arXiv:1508.01316.Google Scholar
  37. [35]
    F. Verstraete and J. I. Cirac, arXiv:cond-mat/0407066.Google Scholar
  38. [36]
    J. Jordan, R. Orús, G. Vidal, F. Verstraete and J. I. Cirac, Phys. Rev. Lett. 101, 250602 (2008).CrossRefADSGoogle Scholar
  39. [37]
    B. Pirvu, F. Verstraete and G. Vidal, Phys. Rev. B 83, 125104 (2011).CrossRefADSGoogle Scholar
  40. [38]
    M. den Nijs and K. Rommelse, Phys. Rev. B 40, 4709 (1989).CrossRefADSGoogle Scholar

Copyright information

© The Korean Physical Society 2016

Authors and Affiliations

  • Xi-Hao Chen
    • 1
  • Sam Young Cho
    • 1
    Email author
  • Huan-Qiang Zhou
    • 1
  • Murray T. Batchelor
    • 2
    • 3
  1. 1.Centre for Modern Physics and Department of PhysicsChongqing UniversityChongqingChina
  2. 2.Centre for Modern PhysicsChongqing UniversityChongqingChina
  3. 3.Mathematical Sciences Institute and Department of Theoretical PhysicsResearch School of Physics and Engineering, Australian National UniversityCanberraAustralia

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