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Quantum Heisenberg antiferromagnet on low-dimensional frustrated lattices

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Abstract

We investigate low-temperature magnetization processes for two frustrated quantum Heisenberg antiferromagnets using the lattice gas model. The emerging discrete degrees of freedom indicate a close relation of the frustrated quantum Heisenberg antiferromagnet to the classical lattice gas with a finite nearestneighbor repulsion or, equivalently, to the Ising antiferromagnet in a uniform magnetic field. Using this relation, we obtain analytic results for thermodynamically large systems in the one-dimensional case. In the two-dimensional case, we simulate systems of the size up to 100×100 sites using the classical Monte Carlo method.

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References

  1. A. Honecker, J. Phys.: Condens. Matter, 11, 4697–4713 (1999); arXiv:cond-mat/9902163v1 (1999); A. Honecker, J. Schulenburg, and J. Richter, J. Phys.: Condens. Matter, 16, S749–S758 (2004); arXiv:cond-mat/0309425v2 (2003); J. Richter, J. Schulenburg, and A. Honecker, “Quantum magnetism in two dimensions: From semi-classical Néel order to magnetic disorder,” in: Quantum Magnetism (Lect. Notes Phys., Vol. 645, U. Schollwöck, J. Richter, D. J. J. Farnell, and R. F. Bishop, eds.), Springer, Berlin (2004), p. 85–153.

    Article  ADS  Google Scholar 

  2. J. Schnack, H.-J. Schmidt, J. Richter, and J. Schulenburg, Eur. Phys. J. B, 24, 475–481 (2001); arXiv:condmat/ 0108432v1 (2001); J. Schulenburg, A. Honecker, J. Schnack, J. Richter, and H.-J. Schmidt, Phys. Rev. Lett., 88, 167207 (2002); arXiv:cond-mat/0108498v2 (2001); J. Richter, J. Schulenburg, A. Honecker, J. Schnack, and H.-J. Schmidt, J. Phys.: Condens. Matter, 16, S779–S784 (2004); J. Richter, Fiz. Nizk. Temp., 31, 918–928 (2005); O. Derzhko, J. Richter, A. Honecker, and H.-J. Schmidt, Fiz. Nizk. Temp., 33, 982–996 (2007); arXiv:cond-mat/0612281v2 (2006); J. Richter and O. Derzhko, “Correlated systems on geometrically frustrated lattices: From magnons to electrons,” in: Condensed Matter Physics in the Prime of the 21st Century: Phenomena, Materials, Ideas, Methods (43rd Karpacz Winter School of Theoretical Physics, Lądek Zdrój, Poland, 5–11 February 2007, J. Jędrzejewski, ed.), World Scientific, Singapore (2008), pp. 237–270.

    Article  ADS  Google Scholar 

  3. M. E. Zhitomirsky and H. Tsunetsugu, Phys. Rev. B, 70, 100403(R) (2004); arXiv:cond-mat/0405578v2 (2004); O. Derzhko and J. Richter, Phys. Rev. B, 70, 104415 (2004); arXiv:cond-mat/0404204v1 (2004); M. E. Zhitomirsky and H. Tsunetsugu, Progr. Theoret. Phys. (Suppl.), No. 160, 361–382 (2005); arXiv:cond-mat/0506327v2 (2005); O. Derzhko and J. Richter, Eur. Phys. J. B, 52, 23–36 (2006); arXiv:cond-mat/0604023v1 (2006).

    Article  ADS  Google Scholar 

  4. J. Richter, O. Derzhko, and T. Krokhmalskii, Phys. Rev. B, 74, 144430 (2006); arXiv:cond-mat/0606806v1 (2006); O. Derzhko, J. Richter, and T. Krokhmalskii, Acta Phys. Polon. A, 113, 433–436 (2008).

    Article  ADS  Google Scholar 

  5. O. Derzhko, T. Krokhmalskii, and J. Richter, Phys. Rev. B, 82, 214412 (2010); arXiv:1009.3828v1 [cond-mat. str-el] (2010).

    Article  ADS  Google Scholar 

  6. A. Honecker, F. Mila, and M. Troyer, Eur. Phys. J. B, 15, 227–233 (2000); arXiv:cond-mat/9910438v2 (1999).

    Article  ADS  Google Scholar 

  7. P. Chen, C.-Y. Lai, and M.-F. Yang, Phys. Rev. B, 81, 020409(R) (2010); arXiv:0910.5081v2 [cond-mat.str-el] (2009).

    ADS  Google Scholar 

  8. H.-J. Schmidt, J. Phys. A, 35, 6545–6555 (2002); arXiv:cond-mat/0203270v1 (2002).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. H.-J. Schmidt, J. Richter, and R. Moessner, J. Phys. A, 39, 10673–10690 (2006); arXiv:cond-mat/0604649v1 (2006).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. E. Müller-Hartmann, and J. Zittartz, Z. Phys. B, 27, 261–266 (1977).

    Article  ADS  Google Scholar 

  11. X. N. Wu and F. Y. Wu, Phys. Lett. A, 144, 123–126 (1990).

    Article  ADS  Google Scholar 

  12. X.-Z. Wang and J. S. Kim, Phys. Rev. Lett., 78, 413–416 (1997).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. S. J. Penney, V. K. Cumyn, and D. D. Betts, Phys. A, 330, 507–518 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  14. R. J. Baxter, Exactly Solved Models in Statistical Mechanics, Acad. Press, London (1982).

    MATH  Google Scholar 

  15. D. J. J. Farnell, R. Zinke, J. Schulenburg, and J. Richter, J. Phys.: Condens. Matter, 21, 406002 (2009); arXiv:0908.2881v1 [cond-mat.str-el] (2009).

    Article  Google Scholar 

  16. T. Ono, H. Tanaka, H. Aruga Katori, F. Ishikawa, H. Mitamura, and T. Goto, Phys. Rev. B, 67, 104431 (2003).

    Article  ADS  Google Scholar 

  17. C. Schröder, H. Nojiri, J. Schnack, P. Hage, M. Luban, and P. Kögerler, Phys. Rev. Lett., 94, 017205 (2005).

    Article  ADS  Google Scholar 

  18. M. Maksymenko, O. Derzhko, and J. Richter, Acta Phys. Polon. A, 119, 860–862 (2011); “Low-temperature properties of the quantum Heisenberg antiferromagnet on some one-dimensional lattices containing equilateral triangles,” Preprint ICMP-10-08E, http://www.icmp.lviv.ua/preprints/2010.html, Inst. Condens. Matter Phys., Lvov (2010).

    Google Scholar 

  19. N. B. Ivanov, Cond. Matter Phys., 12, 435–447 (2009); arXiv:0909.2182v1 [cond-mat.str-el] (2009).

    Article  Google Scholar 

  20. G. Seeber, P. Kögerler, B. M. Kariuki, and L. Cronin, Chem. Commun., 2004, 1580–1581 (2004); N. B. Ivanov, J. Schnack, R. Schnalle, J. Richter, P. Kögerler, G. N. Newton, L. Cronin, Y. Oshima, and H. Nojiri, Phys. Rev. Lett., 105, 037206 (2010); arXiv:1004.2373v1 [cond-mat.str-el] (2010).

    Article  Google Scholar 

  21. J.-B. Fouet, F. Mila, D. Clarke, H. Youk, O. Tchernyshyov, P. Fendley, and R. M. Noack, Phys. Rev. B, 73, 214405 (2006); arXiv:cond-mat/0603609v2 (2006).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Lvov, Ukraine

    O. V. Derzhko & T. E. Krokhmalskii

  2. Ivan Franko National University of Lviv, Lvov, Ukraine

    O. V. Derzhko & T. E. Krokhmalskii

  3. Institut für Theoretische Physik, Otto-von-Guericke-Universitätt Magdeburg, Magdeburg, Germany

    J. Richter

Authors
  1. O. V. Derzhko
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  2. T. E. Krokhmalskii
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  3. J. Richter
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Correspondence to O. V. Derzhko.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 167, No. 2, pp. 441–452, September, 2011.

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Derzhko, O.V., Krokhmalskii, T.E. & Richter, J. Quantum Heisenberg antiferromagnet on low-dimensional frustrated lattices. Theor Math Phys 168, 1236–1245 (2011). https://doi.org/10.1007/s11232-011-0101-3

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