Two-particle correlations in the one-dimensional Hubbard model: a ground-state analytical solution
E. Vallejo1, O. Navarro1, J.E. Espinosa2
1 Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Apartado Postal 70-360, 04510 México D.F., México.
2 Facultad de Ciencias Físico-Matemáticas (Posgrado en Optoelectrónica) BUAP, Puebla Pue., México.
Recibido el 29 de abril de 2002. ]]> Aceptado el 27 de noviembre de 2002.
Abstract
A solution to the extended Hubbard Hamiltonian for the case of two-particles in an infinite one-dimensional lattice is presented, using a real-space mapping method and the Green function technique. This Hamiltonian considers the on-site (U) and the nearest-neighbor (V) interactions. The method is based on mapping the correlated many-body problem onto an equivalent site-impurity tight-binding one in a higher dimensional space. In this new space we obtained the analytical solution for the ground state binding energy. Results are in agreement with the numerical solution obtained previously [1], and with those obtained in the reciprocal space [2].
Keywords: Hubbard model, fermions in reduced dimensions, strongly correlated electron systems.
Resumen
Se resolvió el hamiltoniano de Hubbard extendido para dos partículas en una red unidimensional, usando el método del mapeo en el espacio real y la técnica de la función de Green. Este hamiltoniano considera las interacciones intra-atómicas U e inter-atómicas V. El método mapea el problema de muchos cuerpos correlación de un problema equivalente de amarre fuerte en un espacio de mayor dimensión. Haciendo un análisis del problema en este espacio se obtuvo la solución analítica para la energía de enlace del estado base. Los resultados están en completo acuerdo con la soluciones obtenidas tanto numéricamente [1] como en el espacio recíproco [2].
Palabras clave: Modelo de Hubbard, fermiones en dimensiones reducidas, sistemas electrónicos fuertemente correlacionados.
PACS: 71.10.fd; 71.10Pm; 71.10Li; 71.27.+a
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Acknowledgement
This work was partially supported by grants from CONACyT México 33630-E, from UNAM through IN106600 and by DGEP-UNAM.
References
1. O. Navarro and C. Wang, Rev. Mex. Fís., 38 (1992) 553; [ Links ] O. Navarro, C. Wang, Solid State Commun. 83 (1992) 473; [ Links ] L.A. Perez, O. Navarro and C. Wang, Phys. Rev. B 53 (1996) 15389. [ Links ]
2. F. Marsiglio and J.E. Hirsch, Physica C 171 (1990) 554. [ Links ]
3. E.H. Lieb and F.Y. Wu, Phys. Rev Lett. 20 (1968) 1445. [ Links ]
4. See reprints in Exactly Solvable Models of Strongly Correlated Electrons, edited by V.E. Korepin and F.H.L. Ebler (World Scientific, Singapore, 1994). [ Links ]
5. W. Metzner and D. Vollhardt, Phys. Rev. Lett. 62 (1989) 324. [ Links ]
6. A.M. Tsvelick and P.B. Wiegmann, Adv. Phys. 32 (1983) 453; [ Links ] A.A. Aligia, C.A. Balseiro and C.R. Proetto, Phys. Rev. B 33 (1986) 6476. [ Links ]
7. J. Hubbard, Proc. R. Soc. London Ser. A 276 (1963) 238; [ Links ] M.C. Gutzwiller, Phy. Rev. Lett. 10 (1963) 159. [ Links ]
8. E.H. Lieb, Phys. Rev. Lett. 62 (1989) 1201. [ Links ]
9. N.F. Mott, Metal-Insulator Transition (Taylor & Francis Inc., London, Second Edition 1990). [ Links ]
10. P.W. Anderson, Solid State Physics 14 (1963) 99. [ Links ]
11. S. Caprara, M. Avignon and O. Navarro, Phys. Rev. B 61 (2000) 15667. [ Links ]
12. R. Micnas, J. Ranninger and S. Robaszkiewicz, Rev. Mod. Phys. 62 (1990) 113. [ Links ]
13. A.S. Blaer, H.C. Ren and O. Tchernyshyov, Phys. Rev. B 55 (1997) 6035. [ Links ]
14. S. Fujimoto, Phys. Rev. B64 (2001) 85102. [ Links ]
15. M.W. Long and R. Fehrenbacher, J. Phys.: Condens. Matter 2 (1990) 10343. [ Links ]
16. A.S. Alexandrov, S.V. Traven and P.E. Kornilovitch, J. Phys.: Condens. Matter 4 (1992) L89. [ Links ]
17. D.L. Shepelyansky, Phys. Rev. Lett. 73 (1994) 2607. [ Links ]
18. R. Oviedo-Roa, C. Wang and O. Navarro, J. Low Temp. Phys. 105 (1996) 651. [ Links ]
19. H.Q. Lin and J.E. Hirsch, Phys. Rev. B 52 (1995) 16155. [ Links ]
20. M. Airoldi and A. Parola, Phys. Rev. B51 (1995) 16327. [ Links ]
21. J.E. Espinosa, O. Navarro and M. Avignon, Eur. Phys. J. B 18 (2000) 9. [ Links ]
22. G. Kotliar and A.E. Ruckenstein, Phys. Rev. Lett. 57 (1986) 1362. [ Links ]
23. S. R. White, D. J. Scalapino, R. L. Sugar, and N. E. Bickers, Phys. Rev. Lett. 63 (1989) 1523. [ Links ]
24. J. E. Hirsch, Phys. Rev. B22 (1980) 5259. [ Links ]
25. F. López-Urias and G.M. Pastor, Phys. Rev. B59 (1999) 5223. [ Links ]
26. O. Navarro, Introducción a la Superconductividad, Aula Magna UAS, Vol. 11 (1997). [ Links ]
27. S.A. Trugman, in Applications of Statistical and Field Theory Method to Condensed Matter, Ed. by D. Baeriswyl, et al., (Plenum Press, New York, 1990) p.252. [ Links ]
28. E. N. Economou, Green's Functions in Quantum Physics (Springer Series in Solid State Sciences, Vol.7, Second Edition, 1993). [ Links ]
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