Abstract
Functional integral methods provide a way to define mean-field theories and to systematically improve them. For the Hubbard model and similar strong-correlation problems, methods based in particular on the Hubbard-Stratonovich transformation have however been plagued by difficulties to formulate the problem in a spin-rotation invariant way. Here a formalism circumventing this problem by using a space- and time-dependent spin reference axis is discussed. This formulation is then used to suggest a possible alternative to Nagaoka ferromagnetism in the strongly correlated Hubbard model in the vicinity of half-filling. Finally, some aspects of single-particle spectra in a simplified model for a short-range ordered antiferromagnet are discussed.
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References
P. W. Anderson,Science 235, 1196 (1987).
H. J. Schulz,Phys. Rev. Lett. 64, 1445 (1990).
B. I. Shraiman and E. D. Siggia,Phys. Rev. Lett. 62, 1564 (1989).
J. Hubbard,Phys. Rev. Lett. 3, 77 (1959).
R. L. Stratonovich,Sov. Phys. Dokl. 2, 416 (1958).
H. J. Schulz,Phys. Rev. Lett. 65, 2462 (1990).
H. J. Schulz, inThe Physics and Mathematical Physics of the Hubbard Model, edited by D. K. Campbell (Plenum, New York, ????).
A. A. Gomes and P. Lederer,J. Phys. (Paris) 38, 231 (1977).
see also R. E. Prange and V. Korenman,Phys. Rev. B 19, 4691 (1979), and Z. Y. Weng, C. S. Ting, and T. K. Lee,Phys. Rev. B 43, 3793 (1991).
B. Berg and M. Lüscher,Nucl. Phys. B 190, 412 (1981).
R. Shankar,Nucl. Phys. B 330, 433 (1990).
Y. Nagaoka,Phys. Rev. 147, 392 (1966).
B. Douçot and R. Rammal,Int. J. Mod. Phys. B 3, 1755 (1989).
H. J. Schulz (unpublished).
R. B. Laughlin, Science242, 525 (1988).
P. Lederer, D. Poilblanc, and T. M. Rice,Phys. Rev. Lett. 63, 1519. (1989).
J. A. Riera and A. P. Young,Phys. Rev. B 40, 5285 (1989).
D. Poilblanc,Phys. Rev. B 44, 9562 (1991).
see e.g., P. A. Lee,Phys. Rev. Lett. 63, 680 (1989).