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The phase diagram of the extended anisotropic ferromagnetic-antiferromagnetic Heisenberg chain

  • Solid State and Materials
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Abstract.

By using Density Matrix Renormalization Group (DMRG) technique we study the phase diagram of 1D extended anisotropic Heisenberg model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. We analyze the static correlation functions for the spin operators both in- and out-of-plane and classify the zero-temperature phases by the range of their correlations. On clusters of 64, 100, 200, 300 sites with open boundary conditions we isolate the boundary effects and make finite-size scaling of our results. Apart from the ferromagnetic phase, we identify two gapless spin-fluid phases and two ones with massive excitations. Based on our phase diagram and on estimates for the coupling constants known from literature, we classify the ground states of several edge-sharing materials.

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References

  1. M. Hase, H. Kuroe, K. Ozawa, O. Suzuki, H. Kitazawa, G. Kido, T. Sekine, Phys. Rev. B 70, 104426 (2004)

    Article  ADS  Google Scholar 

  2. S.L. Drechsler, J. Richter, A.A. Gippius, A. Vasiliev, A.A. Bush, A.S. Moskvin, J. Malek, Y. Prots, W. Schnelle, H. Rosner, Europhys. Lett. 73, 83 (2006)

    Article  ADS  Google Scholar 

  3. M. Enderle, C. Mukherjee, B. Fak, R.K. Kremer, J.M. Broto, H. Rosner, S.L. Drechsler, J. Richter, J. Malek, A. Prokofiev et al., Europhys. Lett. 70, 237 (2005)

    Article  ADS  Google Scholar 

  4. H.A. Krug von Nidda, L.E. Svistov, M.V. Eremin, R.M. Eremina, A. Loidl, V. Kataev, A. Validov, A. Prokofiev, W. Aßmus, Phys. Rev. B 65, 13445 (2002)

    Google Scholar 

  5. A.N. Vasil'ev, L.A. Ponomarenko, H. Manaka, I. Yamada, M. Isobe, Y. Ueda, Phys. Rev. B 64, 024419 (2001)

    Article  ADS  Google Scholar 

  6. T. Tonegawa, I. Harada, J. Phys. Soc. Jpn 56, 2153 (1987)

    Article  ADS  Google Scholar 

  7. S. Hirata, K. Nomura, Phys. Rev. B 61, 9453 (2000)

    Article  ADS  Google Scholar 

  8. F.D.M. Haldane, Phys. Rev. B 25, 4925 (1982)

    Article  ADS  Google Scholar 

  9. E. Plekhanov, A. Avella, F. Mancini, Phys. Rev. B 74, 115120 (2006)

    Article  ADS  Google Scholar 

  10. S.R. White, I. Affleck, Phys. Rev. B 54, 9862 (1996)

    Article  ADS  Google Scholar 

  11. C.K. Majumdar, J. Phys. C 3, 911 (1970)

    Article  ADS  Google Scholar 

  12. T. Hamada, J.K.S. Nakagawa, Y. Natsume, J. Phys. Soc. Jpn 57, 1891 (1988)

    Article  ADS  Google Scholar 

  13. F.D.M. Haldane, Phys. Lett. A 93, 464 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  14. F.D.M. Haldane, Phys. Rev. Lett. 50, 1153 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  15. E. Dagotto, Rev. Mod. Phys. 66, 763 (1994)

    Article  ADS  Google Scholar 

  16. H.H. Hung, C.D. Gong, Phys. Rev. B 71, 054413 (2005)

    Article  ADS  Google Scholar 

  17. I. Affleck, in Fields, Strings and Critical Phenomena, edited by E. Brezin, J. Zinn-Justin (North-Holland, Amsterdam, 1990)

  18. H.J. Schultz, in Proceedings of the Les Houches Sunner School LXI: Mesoscopic Quantum Physics, edited by E. Ackermans, G. Montambaux, J.L. Pichard, J. Zinn-Justin (Elsevier, Amsterdam, 1995), p. 533

  19. M. Azuma, Z. Hiroi, M. Takano, K. Ishida, Y. Kitaoka, Phys. Rev. Lett. 73, 3463 (1994)

    Article  ADS  Google Scholar 

  20. K. Kojima, A. Keren, G.M. Luke, B. Nachumi, W.D. Wu, Y.J. Uemura, M. Azuma, M. Takano, Phys. Rev. Lett. 74, 2812 (1995)

    Article  ADS  Google Scholar 

  21. C. Itoi, S. Qin, Phys. Rev. B 63, 224423 (2001)

    Article  ADS  Google Scholar 

  22. K. Nomura, K. Okamoto, J. Phys. A 27, 5773 (1994)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. R.D. Somma, A.A. Aligia, Phys. Rev. B 64, 024410 (2001)

    Article  ADS  Google Scholar 

  24. R. Jafari, A. Langari, Phys. Rev. B 76, 014412 (2007)

    Article  ADS  Google Scholar 

  25. R. Bursill, G.A. Gehring, D.J.J. Farrnell, J.B. Parkinson, T. Xiang, C. Zeng, J. Phys.: Condens. Matter 7, 8605 (1995)

    Article  ADS  Google Scholar 

  26. A.A. Nersesyan, A.O. Gogolin, F.H.L. Essler, Phys. Rev. Lett. 81, 910 (1998)

    Article  ADS  Google Scholar 

  27. M. Kaburagi, H. Kawamura, T. Hikihara, J. Phys. Soc. Jpn 68, 3185 (1999)

    Article  ADS  Google Scholar 

  28. T. Hikihara, M. Kaburagi, H. Kawamura, Phys. Rev. B 63, 174430 (2001)

    Article  ADS  Google Scholar 

  29. T. Hikihara, M. Kaburagi, H. Kawamura, Can. J. Phys. 79, 1581 (2001)

    Article  ADS  Google Scholar 

  30. D.V. Dmitriev, V.Y. Krivnov, Phys. Rev. B 77, 024401 (2008)

    Article  ADS  Google Scholar 

  31. T. Vekua, A. Honecker, H.J. Mikeska, F. Heidrich-Meisner, Phys. Rev. B 76, 174420 (2007)

    Article  ADS  Google Scholar 

  32. F. Heidrich-Meisner, A. Honecker, T. Vekua, Phys. Rev. B 74, 020403 (2006)

    Article  ADS  Google Scholar 

  33. F. Heidrich-Meisner, I.P. McCulloch, A.K. Kolezhuk, Phys. Rev. B 80, 144417 (2009)

    Article  ADS  Google Scholar 

  34. J. Sudan, A. Lüscher, A.M. Läuchli, Phys. Rev. B 80, 140402 (2009)

    Article  ADS  Google Scholar 

  35. N. Kitanine, J.M. Maillet, V. Terras, Nucl. Phys. B 554, 647 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  36. N. Kitanine, J.M. Maillet, V. Terras, Nucl. Phys. B 567, 554 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  37. I. Affleck, J. Phys. A 31, 4573 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. S. Lukyanov, A. Zamolodchikov, Nucl. Phys. B 493, 571 (1997)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  39. A. Avella, F. Mancini, E. Plekhanov, Condens. Matt. Phys. 9, 485 (2006)

    Google Scholar 

  40. E. Plekhanov, A. Avella, F. Mancini, Physica B 403, 1282 (2008)

    Article  ADS  Google Scholar 

  41. S.R. White, Phys. Rev. Lett. 69, 2863 (1992)

    Article  ADS  Google Scholar 

  42. S.R. White, Phys. Rev. B 48, 10345 (1993)

    Article  ADS  Google Scholar 

  43. S. Furukawa, M. Sato, Y. Saiga, S. Onoda, J. Phys. Soc. Jpn 77, 123712 (2008)

    Article  ADS  Google Scholar 

  44. R.O. Kuzian, S.L. Drechsler, Phys. Rev. B 75, 024401 (2007)

    Article  ADS  Google Scholar 

  45. T. Hikihara, L. Kecke, T. Momoi, A. Furusaki, Phys. Rev. B 78, 144404 (2008)

    Article  ADS  Google Scholar 

  46. L. Kecke, T. Momoi, A. Furusaki, Phys. Rev. B 76, 060407 (2007)

    Article  ADS  Google Scholar 

  47. S.L. Drechsler, J. Richter, R. Kuzian, J. Malek, N. Tristan, B. Buchner, A. Moskvin, A. Gippius, A. Vasiliev, O. Volkova et al., J. Mag. Mag. 316, 306 (2007)

    ADS  Google Scholar 

  48. S.L. Drechsler, J. Malek, S. Nishimoto, U. Nitzsche, R. Kuzian, H. Eschrig, H. Rosner, J. Phys. Conf. Ser. 145, 012060 (2009)

    Article  ADS  Google Scholar 

  49. W.E.A. Lorenz, R.O. Kuzian, S.L. Drechsler, W.D. Stein, N. Wizent, G. Behr, J. Malek, U. Nitzsche, H. Rosner, A. Hiess et al., Europhys. Lett. 88, 37002 (2009)

    Article  ADS  Google Scholar 

  50. Y. Mizuno, T. Tohyama, S. Maekawa, T. Osafune, N. Motoyama, H. Eisaki, S. Uchida, Phys. Rev. B 57, 5326 (1998)

    Article  ADS  Google Scholar 

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Correspondence to E. Plekhanov, A. Avella or F. Mancini.

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Plekhanov, E., Avella, A. & Mancini, F. The phase diagram of the extended anisotropic ferromagnetic-antiferromagnetic Heisenberg chain. Eur. Phys. J. B 77, 381–392 (2010). https://doi.org/10.1140/epjb/e2010-00270-7

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  • DOI: https://doi.org/10.1140/epjb/e2010-00270-7

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