Abstract
The ground-state phase diagram of the two-dimensional Falicov-Kimball model with nearest-neighbour and next-nearest-neighbour hoppings has been studied in the perturbative regime where hoppings are small compared with the on-site Coulomb interaction. The phase diagram at fourth-order exhibits a richer structure than the one of the ordinary Falicov-Kimball model.
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References
L. M. Falicov and J. C. Kimball, Phys. Rev. Lett. 22:997 (1969).
D. I. Khomskii, in Quantum Theory of Solids, I. M. Lifshitz, ed. (Mir, Moscow, 1982).
T. Kennedy and E. H. Lieb, Physica A 138:320 (1986).
C. Gruber and N. Macris, Helv. Phys. Acta 69:851 (1996); C. Gruber, In: Mathematical Results in Statistical Mechanics, World Scientific, Singapore, 1999; Jedrzejewski, J. and Lemański, R.: Acta Phys. Polon. B 32:3243 (2001); Freericks, J. K. and Zlatić, V.: cond-mat/0301188.
J. K. Freericks, E. H. Lieb and D. Ueltschi, Comm. Math. Phys. 227:243 (2002).
J. Hubbard, Proc. Roy. Soc. London A 276:238 (1963); A 277:237 (1964); A 281:401 (1964).
Ch. Gruber, N. Macris, A. Messager and D. Ueltschi, J. Stat. Phys. 86:57 (1997).
K. Michielsen, Phys. Rev. B 50:4283 (1994); P. Farkasovsky, cond-mat/9908094; A. Schiller, Phys. Rev. B 60:15660 (1999); K. Michielsen and H. de Raedt, Phys. Rev. B 59:4565 (1999).
J. Wojtkiewicz and R. Lemański, Phys. Rev. B 64:233103 (2001); Acta Phys. Polon. B 32:3467 (2001).
J. Wojtkiewicz, J. Stat. Phys. 112:1149 (2003).
V. Derzhko and J. Jedrzejewski, Physica A 328:449 (2003).
C. Borgs and R. Kotecký, Comm. Math. Phys. 208:575 (2000).
R. Hlubina, S. Sorella, and F. Guinea, Phys. Rev. Lett. 78:1343 (1997); A. Avella, F. Mancini, D. Villani, and H. Matsumoto, Eur. Phys. J. B 20:303 (2001).
R. Lemański and J. Jedrzejewski, Private communication.
Ch. Gruber, R. Kotecký and D. Ueltschi, J. Phys. A: Math. Gen. 33:7857 (2000).
Ch. Gruber, D. Ueltschi and J. Jedrzejewski, J. Stat. Phys. 76:125 (1994).
T. Kennedy, Rev. Math. Phys. 6:901 (1994).
G. I. Watson and R. Lemański, J. Phys.:Condens. Matter 7:9521 (1995).
R. Lemański, J. K. Freericks and G. Banach, Phys. Rev. Lett. 89:196403 (2002).
R. Lemański, J. K. Freericks and G. Banach, J. Stat. Phys. 116:699 (2004).
C. Borgs, R. Kotecký and D. Ueltschi, Comm. Math. Phys. 181:409 (1996); R. Kotecký and D. Ueltschi, Comm. Math. Phys. 206:289 (1999).
N. Datta, R. Fernandez and J. Fröhlich, J. Stat. Phys. 84:455 (1996).
N. Datta, L. Rey-Bellet, J. Fröhlich and R. Fernandez, Helv. Phys. Acta 69:752 (1996).
J. Fröhlich and L. Rey-Bellet, Helv. Phys. Acta 69:821 (1996).
N. Datta, R. Fernandez and J. Fröhlich, J. Stat. Phys. 96:545 (1999).
J. Slawny, In: Phase Transitions and Critical Phenomena vol. 11: C. Domb and J. Lebowitz, eds (Academic Press, London/New York 1987).
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PACS numbers: 71.10.Fd, 71.21.+a, 75.10.Hk, 75.30.Kz
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Wojtkiewicz, J. Phase Diagram of the Two-dimensional t–t′ Falicov-Kimball Model. J Stat Phys 123, 585–600 (2006). https://doi.org/10.1007/s10955-006-9054-6
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DOI: https://doi.org/10.1007/s10955-006-9054-6