Commun. Comput. Phys., 1 (2006), pp. 575-615.


Zero Temperature Numerical Studies of Multiband Lattice Models of Strongly Correlated Electrons

Yong-Qiang Wang 1, Hai-Qing Lin 1*, J. E. Gubernatis 2

1 Department of Physics and the Institute of Theoretical Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong SAR.
2 Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 USA.

Received 25 January 2006; Accepted (in revised version) April 26, 2006

Abstract

Relative to single-band models, multiband models of strongly interacting electron systems are of growing interest because of their wider range of novel phenomena and their closer match to the electronic structure of real materials. In this brief review we discuss the physics of three multiband models (the three-band Hubbard, the periodic Anderson, and the Falicov-Kimball models) that was obtained by numerical simulations at zero temperature. We first give heuristic descriptions of the three principal numerical methods (the Lanczos, the density matrix renormalization group, and the constrained-path Monte Carlo methods). We then present generalized versions of the models and discuss the measurables most often associated with them. Finally, we summarize the results of their ground state numerical studies. While each model was developed to study specific phenomena, unexpected phenomena, usually of a subtle quantum mechanical nature are, often exhibited. Just as often, the predictions of the numerical simulations differ from those of mean-field theories.


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Key words: Lanczos method; density matrix renormalization group; constrained-path Monte Carlo; three-band Hubbard model; periodic Anderson model; Falicov-Kimball model


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Correspondence to: Hai-Qing Lin , Department of Physics and the Institute of Theoretical Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong SAR. Email: hqlin@sun1.phy.cuhk.edu.hk
 

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