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Cluster perturbation theory for spin Hamiltonians

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Abstract

We extend cluster perturbation theory to quantum spin systems. As an application, we calculate the spectral function and the density of states of one-particle excitations of a chain of spin-1/2 particles with alternating exchange interaction.

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References

  1. M. Potthoff, M. Aichhorn, and C. Dahnken, Phys. Rev. Lett., 91, 206402 (2003).

    Article  ADS  Google Scholar 

  2. G. Kotliar, S. Savrasov, G. Pálsson, and G. Biroli, Phys. Rev. Lett., 87, 186401 (2001).

    Article  ADS  Google Scholar 

  3. M. H. Hettler, A. N. Tahvildar-Zadeh, M. Jarrell, T. Pruschke, and H. R. Krishnamurthy, Phys. Rev. B, 58, R7475–R7479 (1998).

    Article  ADS  Google Scholar 

  4. T. Maier, M. Jarrell, T. Pruschke, and M. H. Hettler, Rev. Modern Phys., 77, 1027–1080 (2005).

    Article  ADS  Google Scholar 

  5. C. Gros and R. Valentí, Phys. Rev. B, 48, 418–425 (1993).

    Article  ADS  Google Scholar 

  6. D. Sénéchal, D. Perez, and M. Pioro-Ladrière, Phys. Rev. Lett., 84, 522–525 (2000).

    Article  ADS  Google Scholar 

  7. D. Sénéchal, D. Perez, and D. Plouffe, Phys. Rev. B, 66, 075129 (2002).

    Article  ADS  Google Scholar 

  8. M. H. Hettler, A. N. Tahvildar-Zadeh, M. Jarrell, T. Pruschke, and H. R. Krishnamurthy, Phys. Rev. B, 58, R7475–R7479 (1998).

    Article  ADS  Google Scholar 

  9. A. Tahvildar-Zadeh, M. Jarrell, and J. Freericks, Phys. Rev. B, 55, R3332–R3335 (1997).

    Article  ADS  Google Scholar 

  10. M. G. Zacher, R. Eder, E. Arrigoni, and W. Hanke, Phys. Rev. Lett., 85, 2585–2588 (2002).

    Article  ADS  Google Scholar 

  11. A. Izyumov, F. A. Kassan-ogly, and Yu. N. Skryabin, Field Methods in Theory of Ferromagnetism [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  12. Y. Hosokoshi, Y. Nakazawa, K. Inoue, K. Takizawa, H. Nakano, M. Takahashi, and T. Goto, Phys. Rev. B, 60, 12924–12932 (1999).

    Article  ADS  Google Scholar 

  13. T. Goto, N. V. Mushnikov, Y. Hosokoshi, K. Katoh, and K. Inoue, Phys. B, 329-333, 1160–1161 (2003).

    Article  ADS  Google Scholar 

  14. I. Affleck, Phys. Rev. B, 41, 6697–6702 (1990); T. Giamarchi and A. M. Tsvelik, Phys. Rev. B, 59, 11398-11407 (1999).

    Article  ADS  Google Scholar 

  15. T. M. Rice, Science, 298, 760–761 (2002).

    Article  Google Scholar 

  16. E. Dagotto, Rev. Modern Phys., 66, 763–840 (1994).

    Article  ADS  Google Scholar 

  17. A. I. Larkin, Sov. Phys. JETP, 10, 186–191 (1959).

    MATH  MathSciNet  Google Scholar 

  18. V. G. Vaks, A. I. Larkin, and S. A. Pikin, Sov. Phys. JETP, 24, 240 (1967).

    ADS  Google Scholar 

  19. Yu. A. Izyumov and F. A. Kassan-ogly, Fiz. Met. Metalloved., 26, 385 (1968).

    Google Scholar 

  20. M. A. Savchenko and V. V. Tarasenko, Fiz. Tverd. Tela, 9, 3284 (1967).

    Google Scholar 

  21. S. A. Pikin, Sov. Phys. JETP, 27, 995.

  22. E. M. Pikalev, M. A. Savchenko, and J. Solyom, Sov. Phys. JETP, 28, 734 (1969).

    ADS  Google Scholar 

  23. D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum [in Russian], Nauka, Moscow (1975); English transl., World Scientific, Teaneck, N. J. (1988).

    Google Scholar 

  24. I. G. Bostrem, A. S. Ovchinnikov, and V. E. Sinitsyn, Theor. Math. Phys., 149, 1527–1544 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  25. V. E. Sinitsyn, I. G. Bostrem, and A. S. Ovchinnikov, J. Phys. A, 40, 645–668 (2007).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  26. C. Dahnken, M. Aichhorn, W. Hanke, E. Arrigoni, and M. Potthoff, Phys. Rev. B, 70, 245110 (2004).

    Article  ADS  Google Scholar 

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Correspondence to A. S. Ovchinnikov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 162, No. 2, pp. 216–226, February, 2010.

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Ovchinnikov, A.S., Bostrem, I.G. & Sinitsyn, V.E. Cluster perturbation theory for spin Hamiltonians. Theor Math Phys 162, 179–187 (2010). https://doi.org/10.1007/s11232-010-0013-7

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