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Volume 1, Issue 4
Zero Temperature Numerical Studies of Multiband Lattice Models of Strongly Correlated Electrons

Y. Q. Wang, H. Q. Lin & J. E. Gubernatis

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

Published online: 2006-01

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  • 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.

  • Keywords

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

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COPYRIGHT: © Global Science Press

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@Article{CiCP-1-575, author = {Y. Q. Wang, H. Q. Lin and J. E. Gubernatis}, title = {Zero Temperature Numerical Studies of Multiband Lattice Models of Strongly Correlated Electrons}, journal = {Communications in Computational Physics}, year = {2006}, volume = {1}, number = {4}, pages = {575--615}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7971.html} }
TY - JOUR T1 - Zero Temperature Numerical Studies of Multiband Lattice Models of Strongly Correlated Electrons AU - Y. Q. Wang, H. Q. Lin & J. E. Gubernatis JO - Communications in Computational Physics VL - 4 SP - 575 EP - 615 PY - 2006 DA - 2006/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7971.html KW - Lanczos method KW - density matrix renormalization group KW - constrained-path Monte Carlo KW - three-band Hubbard model KW - periodic Anderson model KW - Falicov-Kimball model AB -

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.

Y. Q. Wang, H. Q. Lin and J. E. Gubernatis. (2006). Zero Temperature Numerical Studies of Multiband Lattice Models of Strongly Correlated Electrons. Communications in Computational Physics. 1 (4). 575-615. doi:
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