Abstract
The asymmetric correlated-hopping Hubbard model is analysed perturbatively for large values of the Coulomb interaction U. An effective Hamiltonian is obtained up to terms of the order U −3. For d=2 and in the limit of the strong asymmetry, the orderings of the ground states are found (confirming earlier nonrigorous results). Their thermal and quantum stability is proved. These results have been obtained by an application of the quantum Pirogov–Sinai theory in the variant developed by Datta, Fernandez, Fröhlich, and Rey-Bellet.
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References
J. Hubbard, Proc. Roy. Soc. London A 276:238(1963)
J. Hubbard, Proc. Roy. Soc. London A 277:237(1964)
J. Hubbard, Proc. Roy. Soc. London A 281:401(1964).
M. C. Gutzwiller, Phys. Rev. A 137:1726(1965).
E. H. Lieb, Advances in Dynamical Systems and Quantum Physics, Proc. of the May 1993 Conference in honour of G. F. Dell'Antonio (World Scientific).
L. M. Falicov and J. C. Kimball, Phys. Rev. Lett. 22:997(1969).
C. Gruber and N. Macris, Helv. Phys. Acta 69:851(1996).
J. Jedrzejewski and R. Lemańnski, Acta Phys. Polon. B 32:3243(2001).
J. K. Freericks, E. H. Lieb, and D. Ueltschi, Comm. Math. Phys. 227:243(2002).
T. Kennedy and E. H. Lieb, Phys. A 138:320(1986).
Ch. Gruber, D. Ueltschi, and J. Jedrzejewski, J. Stat. Phys. 76:125(1994).
T. Kennedy, Rev. Math. Phys. 6:901(1994).
Ch. Gruber, N. Macris, A. Messager, and D. Ueltschi, J. Stat. Phys. 86:57(1997).
K. Haller and T. Kennedy, J. Stat. Phys. 102:15(2001).
J. Spal/ek, Eur. J. Phys. 21:511(2000).
J. E. Hirsch, Physica C 158:236(1989).
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).
A. A. Aligia, L. Arrachea, and E. R. Gagliano, Phys. Rev. B 51:13774(1995).
J. C. Amadon and J. E. Hirsch, Phys. Rev. B 54:6364(1996).
L. Didukh, V. Hankevych, and Yu. Skorenkyy, Physica B 284–288:1537(2000).
M. Kollar and D. Vollhardt, Phys. Rev. B 63:045107(2001).
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).
C. Borgs, R. Kotecky, and D. Ueltschi, Comm. Math. Phys. 181:409(1996).
C. Borgs and R. Kotecky, Comm. Math. Phys. 208:575(2000).
Ch. Gruber, R. Kotecky, and D. Ueltschi, J. Phys. A: Math. Gen. 33:7857(2000).
R. Kotecky and D. Ueltschi, Comm. Math. Phys. 206:289(1999).
A. Messager and S. Miracle-Sole, Rev. Math. Phys. 8:271(1996).
J. Wojtkiewicz and R. Lemańnski, Phys. Rev. B 64:233103(2001).
W. Selke, Phase Transitions and Critical Phenomena, Vol. 14, C. Domb and J. Lebowitz, eds. (Academic Press, London/New York, 1992).
J. Slawny, Phase Transitions and Critical Phenomena, Vol. 11, C. Domb and J. Lebowitz, eds. (Academic Press, London/New York, 1987).
S. A. Pirogov and Ya. G. Sinai, Teor. Mat. Fiz. 25:358(1975)
S. A. Pirogov and Ya. G. Sinai, Teor. Mat. Fiz. 26:61(1976).
W. Holsztynski and J. Slawny, Comm. Math. Phys. 61:177(1978).
P. Farkašovskńy and N. Hudáková, cond-mat/0107105.
U. Brandt, A. Fledderjohann, and G. Hülsenbeck, Z. Phys. B 81:409(1990). V. Zlatińc, J. K. Freericks, R. Lemańnski, and G. Czycholl, Philos. Mag. B 81:409 (2001).
R. Lemańnski and J. Wojtkiewicz, Phys. Stat. Sol. 236:408(2003).
J. Jedrzejewski, Z. Phys. B, Condens. Matter 59:325(1985); J. Jedrzejewski, Physica A 205:702 (1994).
J. Bricmont and J. Slawny, J. Stat. Phys. 54:89(1989).
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Wojtkiewicz, J. Stability of Ground States of 2d Strongly Asymmetric Correlated-Hopping Hubbard Model. Journal of Statistical Physics 112, 1127–1151 (2003). https://doi.org/10.1023/A:1024667609435
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DOI: https://doi.org/10.1023/A:1024667609435