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Continuum of many-particle states near the metal-insulator transition in the Hubbard model

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Abstract

The strong coupling diagram technique is used for investigating states near the metal-insulator transition in the half-filled two-dimensional repulsive Hubbard model. The nonlocal third-order term is included in the irreducible part along with local terms of lower orders. Derived equations for the electron Green’s function are solved by iteration for moderate Hubbard repulsions and temperatures. Starting iteration from Green’s functions of the Hubbard-I approximation with various distances of poles from the real frequency axis continua of different metallic and insulating solutions are obtained. The insulating solutions vary in the width of the Mott gap, while the metallic solutions differ in the shape of the spectral function in the vicinity of the Fermi level. Besides, different scenarios of the metal-insulator transition – with a sudden onset of a band of mobile states near the Fermi level and with gradual closure of the Mott gap – are observed with a change in temperature. In spite of these dissimilarities, all solutions have a common curve separating metallic and insulating states in the phase diagram. Near this curve metallic and insulating solutions coexist. For moderate Hubbard repulsions metallic solutions are not Fermi liquids.

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References

  1. M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998)

    Article  ADS  Google Scholar 

  2. J. Hubbard, Proc. R. Soc. Lond. A 276, 238 (1963)

    Article  ADS  Google Scholar 

  3. J. Hubbard, Proc. R. Soc. Lond. A 277, 237 (1964)

    Article  ADS  Google Scholar 

  4. J. Hubbard, Proc. R. Soc. Lond. A 281, 401 (1964)

    Article  ADS  Google Scholar 

  5. R.O. Zaitsev, Sov. Phys. J. Exp. Theor. Phys. 43, 574 (1976)

    ADS  Google Scholar 

  6. R.O. Zaitsev, Sov. Phys. J. Exp. Theor. Phys. 48, 1193 (1978)

    ADS  Google Scholar 

  7. E.G. Goryachev, E.V. Kuzmin, S.G. Ovchinnikov, J. Phys. C 15, 1481 (1982)

    Article  ADS  Google Scholar 

  8. Yu.A. Izyumov, Yu.N. Skryabin, Statistical Mechanics of Magnetically Ordered Systems (Consultants Bureau, New York, 1988)

  9. A. Georges, G. Kotliar, W. Krauth, M. Rozenberg, Rev. Mod. Phys. 68, 13 (1996)

    Article  ADS  Google Scholar 

  10. H. Park, K. Haule, G. Kotliar, Phys. Rev. Lett. 101, 186403 (2008)

    Article  ADS  Google Scholar 

  11. E. Gull, P. Werner, M. Troyer, A.J. Millis, Europhys. Lett. 84, 37009 (2008)

    Article  ADS  Google Scholar 

  12. M. Balzer, B. Kyung, D. Sénéchal, A.-M.S. Tremblay, M. Potthoff, Europhys. Lett. 85, 17002 (2009)

    Article  ADS  Google Scholar 

  13. M.I. Vladimir, V.A. Moskalenko, Theor. Math. Phys. 82, 301 (1990)

    Article  Google Scholar 

  14. S.I. Vakaru, M.I. Vladimir, V.A. Moskalenko, Theor. Mat. Fiz. 85, 1185 (1990)

    Article  Google Scholar 

  15. W. Metzner, Phys. Rev. B 43, 8549 (1991)

    Article  ADS  Google Scholar 

  16. L. Craco, M.A. Gusmão, Phys. Rev. B 52, 17135 (1995)

    Article  ADS  Google Scholar 

  17. L. Craco, M.A. Gusmão, Phys. Rev. B 54, 1629 (1996)

    Article  ADS  Google Scholar 

  18. V.A. Moskalenko, P. Entel, D.F. Digor, Phys. Rev. B 59, 619 (1999)

    Article  ADS  Google Scholar 

  19. S. Pairault, D. Sénéchal, A.-M.S. Tremblay, Eur. Phys. J. B 16, 85 (2000)

    Article  ADS  Google Scholar 

  20. L. Craco, J. Phys.: Condens. Matter 13, 263 (2001)

    ADS  Google Scholar 

  21. A. Sherman, Phys. Rev. B 73, 155105 (2006)

    Article  ADS  Google Scholar 

  22. A. Sherman, Phys. Rev. B 74, 035104 (2006)

    Article  ADS  Google Scholar 

  23. J. Oitmaa, C. Hamer, W. Zheng, Series Expansion Methods for Strongly Interacting Lattice Models (Cambridge University Press, Cambridge, 2006)

  24. A. Sherman, Physica B 456, 35 (2015)

    Article  ADS  Google Scholar 

  25. A. Sherman, Int. J. Mod. Phys. B 29, 1550088 (2015)

    Article  ADS  Google Scholar 

  26. A. Sherman, Phys. Status Solidi B 252, 2006 (2015)

    Article  ADS  Google Scholar 

  27. A. Sherman, M. Schreiber, Phys. Rev. B 76, 245112 (2007)

    Article  ADS  Google Scholar 

  28. A. Sherman, M. Schreiber, Phys. Rev. B 77, 155117 (2008)

    Article  ADS  Google Scholar 

  29. A. Sherman, J. Magn. Magn. Mater., http://dx.doi.org/10.1016/j.jmmm.2016.12.045

  30. A. Sherman, Eur. Phys. J. B 89, 91 (2016)

    Article  ADS  Google Scholar 

  31. C. Gröber, R. Eder, W. Hanke, Phys. Rev. B 62, 4336 (2000)

    Article  ADS  Google Scholar 

  32. A.A. Abrikosov, L.P. Gor’kov, I.E. Dzyaloshinskii, Methods of Quantum Field Theory in Statistical Physics (Pergamon Press, New York, 1965)

  33. R. Kubo, J. Phys. Soc. Jpn 17, 1100 (1962)

    Article  ADS  Google Scholar 

  34. K.S.D. Beach, R.J. Gooding, F. Marsiglio, Phys. Rev. B 61, 5147 (2000)

    Article  ADS  Google Scholar 

  35. J. Schött, I.L.M. Locht, E. Lundin, O. Grånäs, O. Eriksson, I. Di Marco, Phys. Rev. B 93, 075104 (2016)

    Article  ADS  Google Scholar 

  36. J. Schött, E.G.C.P. van Loon, I.L.M. Locht, M.I. Katsnelson, I. Di Marco, Phys. Rev. B 94, 245140 (2016)

    Article  ADS  Google Scholar 

  37. D. Sénéchal, D. Perez, M. Pioro-Ladrière, Phys. Rev. Lett. 84, 522 (2000)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  39. B. Kyung, S.S. Kancharla, D. Sénéchal, A.-M.S. Tremblay, M. Civelly, G. Kotliar, Phys. Rev. B 73, 165114 (2006)

    Article  ADS  Google Scholar 

  40. O.K. Kalashnikov, E.S. Fradkin, Phys. Status Solidi B 59, 9 (1973)

    Article  ADS  Google Scholar 

  41. S.R. White, Phys. Rev. B 44, 4670 (1991)

    Article  ADS  Google Scholar 

  42. Y.M. Vilk, A.-M.S. Tremblay, J. Phys. I France 7, 1309 (1997)

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Physics, University of Tartu, W. Ostwaldi Str 1, 50411, Tartu, Estonia

    Alexei Sherman

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  1. Alexei Sherman
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Sherman, A. Continuum of many-particle states near the metal-insulator transition in the Hubbard model. Eur. Phys. J. B 90, 120 (2017). https://doi.org/10.1140/epjb/e2017-80082-y

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  • DOI: https://doi.org/10.1140/epjb/e2017-80082-y

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