Abstract.
In this paper, we study the Hubbard model with intersite Coulomb interaction in the ionic limit (i.e. no kinetic energy). It is shown that this model is isomorphic to the spin-1 Ising model in presence of a crystal field and an external magnetic field. We show that for such models it is possible to find, for any dimension, a finite complete set of eigenoperators and eigenvalues of the Hamiltonian. Then, the hierarchy of the equations of motion closes and analytical expressions for the relevant Green's functions and correlation functions can be obtained. These expressions are formal because these functions depend on a finite set of unknown parameters, and only a set of exact relations among the correlation functions can be derived. In the one-dimensional case we show that by means of algebraic constraints it is possible to obtain extra equations which close the set and allow us to obtain a complete exact solution of the model. The behavior of the relevant physical properties for the 1D system is reported.
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References
F. Mancini, Europhys. Lett. 70, 1 (2005)
H. Seo, H. Fukuyama, J. Phys. Soc. Jpn. 77, 2602 (1998)
P. van Dongen, Phy. Rev. B 50, 14016 (1994)
R. Pietig, R. Bulla, S. Blawid, Phys. Rev. Lett. 82, 4046 (1999)
R.H. McKenzie et al., Phys. Rev. B 64, 085109 (2001)
J. Merino, R.H. McKenzie, Phys. Rev. Lett. 87, 237002 (2001)
A. Hoang, P. Thalmeier, J. Phys.: Condens. Matter 14, 6639 (2002)
J. Hirsch, Phys. Rev. Lett. 53, 2327 (1984)
C. Hellberg, J. Appl. Phys. 89, 6627 (2001)
M. Calandra, J. Merino, R.H. McKenzie, Phys. Rev. B 66, 195102 (2002)
M. Blume, Phys. Rev. 141, 517 (1966)
H.W. Capel, Physica (Utrecht) 32, 966 (1966)
H.W. Capel, Physica (Utrecht) 33, 295 (1967)
H.W. Capel, Physica (Utrecht) 37, 423 (1967)
M. Blume, V.J. Emery, R.D. Griffiths, Phys. Rev. A 4, 1071 (1971)
D. Furman, S. Dattagupta, R.B. Griffiths, Phys. Rev. B 15, 441 (1977)
M. Suzuki, B. Tsujiyama, S. Katsura, J. Math. Phys. 8, 124 (1967)
A. Hintermann, F. Rys, Helv. Phys. Acta 42, 608 (1969)
T. Obokata, T. Oguchi, J. Phys. Soc. Jpn 25, 322 (1968)
K.G. Chakraborty, J.W. Tucker, J. Magn. Matter 54-57, 1349 (1986)
A. Rosengren, R. Haggkvist, Phys. Rev. Lett. 63, 660 (1989)
J. Bernasconi, F. Rys, Phys. Rev. B 4, 3045 (1971)
D. Mukamel, M. Blume, Phys. Rev. A 10, 610 (1974)
J. Lajzerowicz, J. Sivardière, Phys. Rev. A 11, 2079 (1975)
J. Sivardière, J. Lajzerowicz, Phys. Rev. A 11, 2090 (1975)
J. Sivardière, J. Lajzerowicz, Phys. Rev. A 11, 2101 (1975)
W. Hoston, A.N. Berker, Phys. Rev. Lett. 67, 1027 (1991)
E.K. Riedel, F.J. Wegner, Phys. Rev. B 9, 294 (1974)
A.N. Berker, M. Wortis, Phys. Rev. B 14, 4946 (1976)
T.W. Burkhardt, Phys. Rev. B 14, 1196 (1976)
T.W. Burkhardt, H.J.F. Knops, Phys. Rev. B 15, 1602 (1977)
G.D. Mahan, S.M. Girvin, Phys. Rev. B 17, 4411 (1978)
M. Kaufman, R.B. Griffiths, J.M. Yeomans, M. Fisher, Phys. Rev. B 23, 3448 (1981)
J.M. Yeomans, M.E. Fisher, Phys. Rev. B 24, 2825 (1981)
J. Oitmaa, J. Phys. C 5, 435 (1972)
P.F. Fox, D.S. Gaunt, J. Phys. C 5, 3085 (1972)
D.M. Saul, M. Wortis, Phys. Rev. B 9, 4964 (1974)
S.L. Lock, B.S. Lee, Phys. Status Solidi B 124, 593 (1984)
M. Tanaka, T. Kawabe, J. Phys. Soc. Jpn. 54, 2194 (1985)
L. Wang, C. Wentworth, J. Appl. Phys. 61, 4411 (1987)
L. Wang, F. Lee, J.D. Kimel, Phys. Rev. B 36, 8945 (1987)
A. Rachadi, A. Benyoussef, Phys. Rev. B 68, 064113 (2003)
S. Grollau, E. Kierlik, M.L. Rosinberg, G. Tarjus, Phys. Rev. E 63, 041111 (2001)
S. Grollau, Phys. Rev. E 65, 056130 (2002)
S. Krinsky, D. Furman, Phys. Rev. B 11, 2602 (1975)
X.D. Mi, Z.R. Yang, Phys. Rev. E 49, 3636 (1994)
B.G.S. Doman, D. ter Haar, Phys. Lett. 2, 15 (1962)
R.A. Tahir-Kheli, B.G.S. Doman, D. ter Haar, Phys. Lett. 4, 5 (1963)
B.G.S. Doman, Phys. Lett. 4, 156 (1963)
H.B. Callen, Phys. Lett. 4, 161 (1963)
M. Suzuki, Phys. Lett. 19, 267 (1965)
T. Oguchi, I. Ono, Prog. Theor. Phys. 35, 998 (1966)
S.V. Tyablikov, V.K. Fedyanin, Fisika metallov and metallovedenie 23, 193 (1967)
R.A. Tahir-Kheli, Phys. Rev. 169, 517 (1968)
O.K. Kalashnikov, E.S. Fradkin, Sov. Phys. JETP 28, 976 (1969)
F.B. Anderson, Phys. Rev. B 3, 3950 (1971)
G.B. Taggart, Phys. Rev. B 20, 3886 (1979)
R. Honmura, T. Kaneyoshi, Prog. Theor. Phys. 60, 635 (1978)
A.F. Siqueira, I.P. Fittipaldi, Phys. Rev. B 31, 6092 (1985)
F. Mancini, A. Avella, Eur. Phys. J. B 37, 37 (2003)
F. Mancini, in Highlights in Condensed Matter Physics, edited by A. Avella, R. Citro, C. Noce, M. Salerno (American Institute of Physics, New York, 2003), 240
F. Mancini, A. Avella, Adv. Phys. 53, 537 (2004)
F. Mancini, Phys. Lett. A 249, 231 (1998)
F. Mancini, Eur. Phys. J. B 45, 497 (2005)
A.J. Fedro, Phys. Rev. B 14, 2983 (1976)
D. Vollhardt, Phys. Rev. Lett. 78, 1307 (1997)
F. Mancini, H. Matsumoto, D. Villani, J. Phys. Studies 3, 474 (1999)
Y.Z. Zhang, T. Minh-Tien, V. Yushankhai, P. Thalmeier (2004), e-print arXiv:cond-mat/0411539
F. Mancini, Tech. Rep., University of Salerno (2005)
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Mancini, F. The extended Hubbard model in the ionic limit. Eur. Phys. J. B 47, 527–540 (2005). https://doi.org/10.1140/epjb/e2005-00357-2
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DOI: https://doi.org/10.1140/epjb/e2005-00357-2