Electronic Correlations within Fermionic Lattice Models

• Authors: M. Matlak , B. Grabiec , S. Krawiec
• Languages of publication: EN

Abstracts

EN

We investigate two-site electronic correlations within generalized Hubbard model, which incorporates the conventional Hubbard model (parameters: t (hopping between nearest neighbours), U (Coulomb repulsion (attraction))) supplemented by the intersite Coulomb interactions (parameters: J^{(1)} (parallel spins), J^{(2)} (antiparallel spins)) and the hopping of the intrasite Cooper pairs (parameter: V). As a first step we find the eigenvalues E_α and eigenvectors |E_α〉 of the dimer and we represent each partial Hamiltonian E_α|E _α〉〈 E_α| (α=1,2,...,16) in the second quantization with the use of the Hubbard and spin operators. Each dimer energy level possesses its own Hamiltonian describing different two-site interactions which can be active only in the case when the level will be occupied by the electrons. A typical feature is the appearance of two generalized t-J interactions ascribed to two different energy levels which do not vanish even for U=J^{(1)}=J{(2)}=V=0 and their coupling constants are equal to ±t in this case. In the large linebreak U-limit for J^{(1)}=J^{(2)}=V=0 there is only one t-J interaction with coupling constant equal to 4t^2/|U| as in the case of a real lattice. The competition between ferromagnetism, antiferromagnetism and superconductivity (intrasite and intersite pairings) is also a typical feature of the model because it persists in the case U=J^{(1)}=J^{(2)}=V=0 and t≢0. The same types of the electronic, competitive interactions are scattered between different energy levels and therefore their thermodynamical activities are dependent on the occupation of these levels. It qualitatively explains the origin of the phase diagram of the model. We consider also a real lattice as a set of interacting dimers to show that the competition between magnetism and superconductivity seems to be universal for fermionic lattice models.

Keywords

EN

71.10.-w; 71.10.Ca; 71.10.Fd; 71.20.Be; 71.27.+a; 71.28.+d; 73.21.La; 78.67.Bf

Discipline

• 78.67.Bf: Nanocrystals, nanoparticles, and nanoclusters
• 71.27.+a: Strongly correlated electron systems; heavy fermions
• 71.10.-w: Theories and models of many-electron systems
• 71.20.Be: Transition metals and alloys
• 71.10.Ca: Electron gas, Fermi gas
• 71.10.Fd: Lattice fermion models (Hubbard model, etc.)
• 73.21.La: Quantum dots
• 71.28.+d: Narrow-band systems; intermediate-valence solids(for magnetic aspects, see 75.20.Hr and 75.30.Mb in magnetic properties and materials)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2007
• Volume: 112
• Issue: 3
• Pages: 537-547

Dates

published

2007-09

received

2007-07-10

Contributors

author

M. Matlak

• Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice, Poland

author

B. Grabiec

• Institute of Physics, University of Zielona Góra, Prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland

author

S. Krawiec

• Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice, Poland

References

• 1. J. Hubbard, Proc. R. Soc. A, 276, 238, 1963; 281, 401, 1964
• 2. M.C. Gutzwiller, Phys. Rev. Lett., 10, 59, 1963
• 3. J. Kanamori, Prog. Theor. Phys., 30, 275, 1963
• 4. C. Herring, in: Magnetism, Vol. IV, Eds. G.T. Rado, H. Suhl, Academic Press, New York 1966, p. 1
• 5. J. Friedel, in: The Physics of Metals, Ed. J.M. Ziman, Cambridge University Press, Cambridge 1969, p. 340
• 6. B. Brandow, Adv. Phys., 26, 651, 1977
• 7. T. Moriya, Spin Fluctuations in Itinerant Electron Magnetism, Springer Series in Solid State Sciences, Vol. 56, Springer, Berlin 1985
• 8. W. Nolting, Quantentheorie des Magnetismus, Vol. 1 and 2, Teubner, Stuttgart 1986
• 9. Metallic Magnetism, Ed. H. Capelmann, Springer Topics in Current Physics, Vol. 42, Springer, Berlin 1987
• 10. N.F. Mott, Metal-Insulator Transitions, Taylor and Francis, London 1990
• 11. P.A. Cox, Transition Metal Oxides, International Series of Monographs on Chemistry, Vol. 27, Clarendon Press, Oxford 1992
• 12. D.E. Logan, Y.H. Szczech, M.E. Tusch, in: Metal-Insulator Transitions Revisited, Eds. P.P. Edwards, C.N.R. Rao, Taylor and Francis, London 1995, p. 395
• 13. P. Fulde, Electron Correlations in Molecules and Solids, Springer, Berlin 1995
• 14. T. Herrmann, W. Nolting, J. Magn. Magn. Mater., 170, 253, 1997
• 15. F. Gebhard, The Mott Metal-Insulator Transitions, Springer Tracts in Modern Physics, Vol. 137, Springer, Berlin 1997
• 16. M. Imada, A. Fujimori, Rev. Mod. Phys., 70, 1039, 1998
• 17. P.W. Anderson, Phys. Rev., 124, 41, 1961
• 18. C. Varma, Y. Yafet, Phys. Rev. B, 13, 2950, 1976
• 19. D. Vollhardt, Rev. Mod. Phys., 56, 99, 1984
• 20. D. Vollhardt, P. Woelfle, P.W. Anderson, Phys. Rev. B, 35, 6703, 1987
• 21. D. Vollhardt, P. Woelfle, The Superfluid Phases of Helium-3, Taylor and Francis, London 1990
• 22. Electronic Properties of Fullerenes, Eds. H. Kuzmany, J. Fink, M. Mehring, S. Roth, Springer Series in Solid State Sciences, Vol. 117, Springer, Berlin 1993
• 23. S. Chakravarty, M.P. Gelfand, S. Kivelson, Science, 254, 970, 1991
• 24. S.L. Sondhi, M.P. Gelfand, H.Q. Lin, D.K. Campbell, Phys. Rev. B, 51, 593, 1995
• 25. S. Robaszkiewicz, R. Micnas, K.A. Chao, Phys. Rev. B, 23, 1447, 1981; 26, 3915, 1982
• 26. J. Ranninger, S. Robaszkiewicz, Physica B, 135, 486, 1985
• 27. A.S. Alexandrov, J. Ranninger, S. Robaszkiewicz, Phys. Rev. B, 33, 4526, 1986
• 28. P.W. Anderson, Science, 235, 1196, 1987
• 29. G. Baskaran, P.W. Anderson, Phys. Rev. B, 37, 580, 1988
• 30. R. Micnas, J. Ranninger, S. Robaszkiewicz, Phys. Rev. B, 37, 9410, 1988; B, 39, 11653, 1989
• 31. G.T. Zimanyi, S.A. Kivelson, A. Luther, Phys. Rev. Lett., 1960, 2089, 1988
• 32. M. Inui, S. Doniach, P.J. Hirschfeld, A.E. Rueckenstein, Phys. Rev. B, 37, 2320, 1988
• 33. R. Micnas, J. Ranninger, S. Robaszkiewicz, Rev. Mod. Phys., 62, 113, 1990
• 34. P.G.J. van Dongen, Phys. Rev. Lett., 67, 757, 1991
• 35. G.A. Lara, G.G. Cabrera, Phys. Rev. B, 47, 14417, 1993
• 36. Y.Z. Yan, Phys. Rev. B, 48, 7140, 1993
• 37. E. Dagotto, Rev. Mod. Phys., 66, 763, 1994
• 38. P.G.J. van Dongen, Phys. Rev. B, 50, 14031, 1994
• 39. A.B. Eriksson, T. Einarson, S. Ostlund, Phys. Rev. B, 52, 3662, 1995
• 40. B.R. Bulka, S. Robaszkiewicz, Phys. Rev. B, 54, 13138, 1996
• 41. H. Tasaki, J. Phys. C, 10, 4378, 1998
• 42. G.I. Japaridze, A.P. Kampf, Phys. Rev. B, 59, 12822, 1999
• 43. R. Micnas, S. Robaszkiewicz, B. Tobijaszewska, J. Supercond., 12, 79, 1999
• 44. G.I. Japaridze, E. Muller-Hartmann, Phys. Rev. B, 61, 113, 2000
• 45. J.X. Zhu, C.S. Ting, Phys. Rev. B, 61, 1456, 2000
• 46. M. Imada, M. Kohno, Phys. Rev. Lett., 84, 143, 2000
• 47. G.I. Japaridze, A.P. Kampf, M. Sekania, P. Kakashvilli, B. Brune, Phys. Rev. B, 65, 14518, 2001
• 48. J. Mizia, G. Górski, K. Kucab, Phys. Status Solidi B, 229, 1221, 2002
• 49. R. Micnas, S. Robaszkiewicz, A. Bussmann-Holder, Phys. Rev. B, 66, 104516, 2002
• 50. R. Micnas, B. Tobijaszewska, J. Phys. C, 14, 9631, 2002
• 51. G. Baskaran, Phys. Rev. Lett., 91, 097003, 2003
• 52. C. Dziurzik, G.I. Japaridze, A. Schadschneider, J. Zittartz, Eur. Phys. J. B, 37, 453, 2004
• 53. W.R. Czart, S. Robaszkiewicz, Acta Phys. Pol. A, 106, 709, 2004
• 54. M. Bak, Phys. Status Solidi B, 242, 420, 2005
• 55. B. Tobijaszewska, R. Micnas, Phys. Status Solidi B, 242, 468, 2005
• 56. W.R. Czart, S. Robaszkiewicz, Phys. Status Solidi B, 243, 151, 2006
• 57. W.R. Czart, S. Robaszkiewicz, Acta Phys. Pol. A, 109, 577, 2006
• 58. I.O. Kulik, A.G. Pedan, Zh. Eksp. Teor. Fiz., 79, 1469, 1980
• 59. K.A. Penson, M. Kolb, Phys. Rev. B, 33, 1663, 1986
• 60. S. Robaszkiewicz, B.R. Bulka, Phys. Rev. B, 59, 6430, 1999
• 61. M. Nakamura, Phys. Rev. B, 61, 16377, 2000
• 62. W.R. Czart, S. Robaszkiewicz, Phys. Rev. B, 64, 104511, 2001
• 63. M. Mierzejewski, M. Maśka, Phys. Rev. B, 69, 054502, 2004
• 64. P.W. Anderson, Phys. Rev., 115, 2, 1959
• 65. P.W. Anderson, in: Solid State Physics, Eds. F. Seitz, D. Turnbull, Vol. 14, Academic Press, New York 1963, p. 99
• 66. D.J. Klein, W.A. Seitz, Phys. Rev. B, 8, 2236, 1973
• 67. J. Florencio, Jr, K.A. Chao, Phys. Rev. Lett., 35, 741, 1975
• 68. W. Kohn, Phys. Rev., 133, 171, 1964
• 69. A.B. Harris, R.V. Lange, Phys. Rev., 157, 295, 1967
• 70. T.A. Kaplan, R.A. Bari, J. Appl. Phys., 41, 875, 1970
• 71. J. Florencio, Jr, K.A. Chao, Phys. Rev. B, 14, 3121, 1976
• 72. K.A. Chao, J. Spalek, A.M. Oleś, J. Phys. C, 10, L271, 1977; Phys. Status Solidi B, 84, 747, 1977; Phys. Rev. B, 18, 3453, 1980
• 73. J. Spalek, A.M. Oleś, Physica B, 86-88, 375, 1977
• 74. J. Spalek, K.A. Chao, J. Phys. C, 13, 5241, 1980
• 75. V.C. Cheng, S.H. Chen, Physica B, 85, 299, 1977
• 76. M. Matlak, Phys. Status Solidi B, 99, K87, 1980
• 77. B. Lorenz, Phys. Status Solidi B, 119, 555, 1983
• 78. L.M. Falicov, R.H. Victor, Phys. Rev. B, 30, 1695, 1984
• 79. J. Callaway, D.P. Chen, R. Tang, Phys. Rev. B, 35, 3705, 1987
• 80. J. Callaway, D.P. Chen, Y. Zhang, Phys. Rev. B, 36, 2084, 1987
• 81. S. Sachdev, R.N. Blatt, Phys. Rev. B, 41, 9323, 1990
• 82. G.M. Pastor, R. Hirsch, B. Muhlschlegel, Phys. Rev. B, 53, 10382, 1996
• 83. D. Senechal, D. Perez, M. Pioto-Ladriere, Phys. Rev. Lett., 84, 522, 2000
• 84. K. Park, S. Sachdev, Phys. Rev. B, 64, 184510, 2001
• 85. E.H. Lieb, F.Y. Wu, Phys. Rev. Lett., 20, 1445, 1968
• 86. A. Klumper, A. Schadschneider, J. Zittartz, Europhys. Lett., 24, 293, 1993
• 87. R. Strack, D. Vollhardt, Phys. Rev. Lett., 70, 2637, 1993
• 88. J. de Boer, A. Schadschneider, Phys. Rev. Lett., 75, 4298, 1995
• 89. A. Montorsi, D.K. Campbell, Phys. Rev. B, 53, 5153, 1996
• 90. Z. Szabo, Phys. Rev. B, 59, 10007, 1999
• 91. C. Dziurzik, A. Schadschneider, J. Zittartz, Eur. Phys. J. B, 12, 109, 1999
• 92. M. Beccaria, Eur. Phys. J. B, 14, 523, 2000
• 93. B. Grabiec, M. Matlak, Acta Phys. Pol. A, 101, 537, 549, 2002
• 94. M. Matlak, J. Aksamit, B. Grabiec, W. Nolting, Ann. Phys., 12, 304, 2003
• 95. E.C. Carter, A.J. Schofield, Phys. Rev. B, 70, 045107, 2004
• 96. M. Matlak, T. Slomska, B. Grabiec, Phys. Status Solidi B, 242, 317, 337, 2005
• 97. D. Bimberg, M. Grundmann, N.N. Ledentsov, Quantum Dot Heterostructures, Wiley, New York 1999
• 98. D. Loos, D.P. Di Vincenzo, Phys. Rev. A, 57, 120, 1998
• 99. J.I. Martin, J. Nogues, K. Liu, J.L. Vicent, I.K. Schuler, J. Magn. Magn. Mater., 256, 449, 2003
• 100. F. Baletto, R. Ferrando, Rev. Mod. Phys., 77, 371, 2004

Identifiers

DOI

10.12693/APhysPolA.112.537