Abstract
We show that the limit of large dimensions (d=∞) can be used to obtain accurate variational results even for low dimensional (d=1, 2) fermionic systems, such as the Hubbard model or the periodic Anderson model. Using explicit correlated variational wave functions this is achieved by evaluating the expectation values for d=∞ with the correct d-dimensional density of states and including 1/d-corrections. For example, an application of this approach to the periodic Anderson model in d=1 shows that the result for the ground state energy, the momentum distributions of c- and f-electrons, and the spin-spin and density-density correlations functions for the f-electrons are in excellent agreement with the variational Monte Carlo data of Shiba.
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References
For a brief review, see D. Vollhardt, inInteracting Electrons in Reduced Dimensions, eds. D. Baeriswyl and D. Campbell (Plenum Press, New York, 1989), p. 107.
M. C. Gutzwiller,Phys. Rev. Lett. 10, 159 (1963);Phys. Rev. A 137, 1726 (1965).
For a brief review, see D. Vollhardt, P. G. J. van Dongen, F. Gebhard, and W. Metzner,Mod. Phys. Lett. B 4, 499 (1990).
W. Metzner and D. Vollhardt,Phys. Rev. Lett. 59, 121 (1987);Phys. Rev. B 37, 7382 (1988).
W. Metzner and D. Vollhardt,Phys. Rev. Lett. 62, 324 (1989).
For recent reviews, see E. Müller-Hartmann,Int. J. Mod. Phys. B 3, 2169 (1989); D. Vollhardt,Physica B 169, 277 (1991).
W. Metzner,Z. Phys. B 77, 253 (1989).
F. Gebhard, Doctoral Thesis, RWTH Aachen, 1990 (unpublished).
F. Gebhard,Phys. Rev. B 41, 9452 (1990).
P. Fazekas, B. Menge, and E. Müller-Hartmann,Z. Phys. B 78, 69 (1990).
W. Metzner,Z. Phys. B 82, 183 (1991).
P. van Dongen, F. Gebhard, and D. Vollhardt,Z. Phys. B 76, 199 (1989).
F. Gebhard and D. Vollhardt, inInteracting Electrons In Reduced Dimensions, eds. D. Baeriswyl and D. Campbell (Plenum Press, New York, 1989), p. 123.
H. Yokoyama and H. Shiba,J. Phys. Soc. Jpn,56, 1490 (1987);56, 3570 (1987).
H. Yokoyama and H. Shiba,J. Phys. Soc. Jpn. 56, 3582 (1987).
T. M. Rice and K. Ueda,Phys. Rev. Lett. 55, 995 (1985);55, 2093 (E) (1985);Phys. Rev. 34, 6420 (1986).
B. H. Brandow,Phys. Rev. B 33, 215 (1986).
H. Shiba,J. Phys. Soc. Jpn. 55, 2765 (1986).
19. H. Shiba, private communication.
G. Kotliar and A. Ruckenstein,Phys. Rev. Lett. 57, 1362 (1986).
This is similar to the approach by D. Baeriswyl [inNonlinearity in Condesnsed Matter, eds. R. Bishopet al., Springer Series in Solid State Sciences, Vol. 69 (Springer, Berlin 1987), p. 103] who thereby constructed a VWF for thed=1 Hubbard model to lowest order int/U.
U. Wolff,Nucl. Phys. B 225, [FS9] 391 (1983).
E. Müller-Hartmann,Z. Phys. B 74, 507 (1989).
E. H. Lieb and F. Y. Wu,Phys. Rev. Lett. 20, 1445 (1968).
See for example, P. A. Lee, T. M. Rice, J. W. Serene, L. J. Sham, and J. W. Wilkins,Comments Cond. Matt. Phys. 12, 99 (1986).
F. Gebhard,Phys. Rev. B 44, 992 (1991).
C. M. Varma, W. Weber, and L. J. Randall,Phys. Rev. B 33, 1015 (1985).
P. Fazekas and B. H. Brandow,Phys. Scripta 36, 809 (1987).
V. Z. Vulović and E. Abrahams,Phys. Rev. B 36, 2614 (1987).
F. Gebhard and D. Vollhardt,Phys. Rev. Lett. 59, 1472 (1987);Phys. Rev. 37, 7382 (1988).
T. Yanagisawa,Phys. Rev. B 37, 2050 (1988).
P. van Dongen and D. Vollhardt,Phys. Rev. Lett. 65, 1663 (1990).
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Dedicated to L. Tewordt on the occasion of his 65th birthday.
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Strack, R., Vollhardt, D. Variational investigation of low dimensional correlated electron systems via the limit of high dimensions. J Low Temp Phys 84, 357–380 (1991). https://doi.org/10.1007/BF00683525
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DOI: https://doi.org/10.1007/BF00683525