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Charge-Stripe Phases Versus a Weak Anisotropy of Nearest-Neighbor Hopping

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Abstract

Recently, we demonstrated rigorously the stability of charge-stripe phases in 2D quantum-particle systems that are described by extended Falicov–Kimball Hamiltonians, with the quantum hopping particles being either spinless fermions or hardcore bosons. In this paper, by means of the same methods, we show that an arbitrary small anisotropy of nearest-neighbor hopping eliminates the π/2-rotation degeneracy of dimeric and axial-stripe phases and orients them in the direction of the weaker hopping. Due to the same anisotropy the obtained phase diagrams of fermions show a tendency to become similar to those of hardcore bosons.

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References

  1. V. Derzhko and J. Jędrzejewski, Formation of charge-stripe phases in a system of spinless fermions or hardcore bosons. Physica A 349:511 (2005).

    Article  ADS  Google Scholar 

  2. J. M. Tranquada, D. J. Buttrey, V. Sachan and J. E. Lorenzo, Simultaneous ordering of holes and spins in La2NiO4.125. Phys. Rev. Lett. 73:1003 (1994).

    Article  ADS  Google Scholar 

  3. J. M. Tranquada, B. J. Sternlieb, J. D. Axe, Y. Nakamura and S. Uchida, Evidence for stripe correlations of spins and holes in copper oxide superconductors. Nature (Lond.) 375:561 (1995).

    Article  ADS  Google Scholar 

  4. A. M. Oleś, Stripe phases in high-temperature superconductors. Acta Phys. Polonica B 31:2963 (2000).

    ADS  Google Scholar 

  5. N. G. Zhang and C. L. Henley, Stripes and holes in a two-dimensional model of spinless fermions or hardcore bosons. Phys. Rev. B 68:014506 (2003).

    Article  ADS  Google Scholar 

  6. C. L. Henley and N. G. Zhang, Spinless fermions and charged stripes at the strong-coupling limit. Phys. Rev. B 63:233107 (2001).

    Article  ADS  Google Scholar 

  7. R. Lemański, J. K. Freericks and G. Banach, Stripe phases in the two-dimensional Falicov–Kimball model. Phys. Rev. Lett. 89:196403 (2002).

    Article  ADS  Google Scholar 

  8. R. Lemański, J. K. Freericks and G. Banach, Charge stripes due to electron correlations in the two-dimensional spinless Falicov–Kimball model. J. Stat. Phys. 116:699 (2004).

    Article  Google Scholar 

  9. U. Brandt and R. Schmidt, Exact results for the distribution of the f-level ground state occupation in the spinless Falicov–Kimball model. Z. Phys. B 63:45 (1986).

    Article  Google Scholar 

  10. T. Kennedy and E. H. Lieb, An itinerant electron model with crystalline or magnetic long range order. Physica A 138:320 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  11. B. Normand and A. P. Kampf, Lattice anisotropy as the microscopic origin of static stripes in cuprates. Phys. Rev. B 64:024521 (2001).

    Article  ADS  Google Scholar 

  12. B. Normand and A. P. Kampf, Supression of static stripe formation by next-neighbor hopping. Phys. Rev. B 65:020509(R) (2001).

    Article  Google Scholar 

  13. M. Raczkowski, B. Normand and A. M. Oleś, Vertical and diagonal stripes in the extended Hubbard model. Phys. Stat. Sol. (b) 236:376 (2003).

    Article  ADS  Google Scholar 

  14. V. Derzhko and J. Jędrzejewski, Charge-stripe phases versus a weak anisotropy of nearest-neighbor hopping, arXiv:cond-mat/0509698

  15. L. M. Falicov and J. C. Kimball, Simple model for semiconductor-metal transitions: SmB 6 and transition-metal oxides. Phys. Rev. Lett. 22:997 (1969).

    Article  ADS  Google Scholar 

  16. C. Gruber and N. Macris, The Falicov–Kimball model: A review of exact results and extensions. Helv. Phys. Acta 69:850 (1996).

    MATH  MathSciNet  Google Scholar 

  17. J. Jędrzejewski and R. Lemański, Falicov–Kimball models of collective phenomena in solids (a concise guide). Acta Phys. Pol. B 32:3243 (2001).

    Google Scholar 

  18. C. Gruber and D. Ueltschi, The Falicov–Kimball model, arXiv:math-ph/0502041.

  19. C. Gruber, J. Jędrzejewski and P. Lemberger, Ground states of the spinless Falicov–Kimball model. II. J. Stat. Phys. 66:913 (1992).

    Article  Google Scholar 

  20. N. Datta, R. Fernández and Jürg FrÖhlich, Effective Hamiltonians and phase diagrams for tight-binding models. J. Stat. Phys. 96:545 (1999).

    Article  MATH  Google Scholar 

  21. C. Gruber, N. Macris, A. Messager and D. Ueltschi, Ground states and flux configurations of the two-dimensional Falicov–Kimball model. J. Stat. Phys. 86:57 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  22. J. Slawny, Low-temperature properties of classical lattice systems: Phase transitions and phase diagrams, In: C. Domb and J. Lebowitz (Eds.), Phase Transitions and Critical Phenomena vol. 11, (Academic Press, London/New York 1985).

    Google Scholar 

  23. T. Kennedy, Some rigorous results on the ground states of the Falicov–Kimball model. Rev. Math. Phys. 6:901 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  24. V. Derzhko and J. Jędrzejewski, From phase separation to long-range order in a system of interacting electrons. Physica A 328:449 (2003).

    Article  ADS  Google Scholar 

  25. R. T. Rockafellar, Convex Analysis, Princeton University Press, 1979.

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Authors and Affiliations

  1. Institute of Theoretical Physics, University of Wrocław, pl. Maksa Borna 9, 50–204, Wrocław, Poland

    V. Derzhko & J. Jedrzejewski

Authors
  1. V. Derzhko
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  2. J. Jedrzejewski
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Correspondence to V. Derzhko.

Additional information

PACS numbers: 71.10.Fd, 71.10.−w, 71.27.+a, 67.40.Db

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Derzhko, V., Jedrzejewski, J. Charge-Stripe Phases Versus a Weak Anisotropy of Nearest-Neighbor Hopping. J Stat Phys 126, 467–505 (2007). https://doi.org/10.1007/s10955-006-9245-1

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  • DOI: https://doi.org/10.1007/s10955-006-9245-1

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