Cluster perturbation theory is a technique for calculating the spectral weight of Hubbard models of strongly correlated electrons, which combines exact diagonalizations on small clusters with strong-coupling perturbation theory at leading order. It is exact in both the strong- and weak-coupling limits and provides a good approximation to the spectral function at any wave vector. Following the paper by S\'en\'echal et al. [Phys. Rev. Lett. $84,$ 522 (2000)], we provide a more complete description and derivation of the method. We illustrate some of its capabilities, in particular regarding the effect of doping, the calculation of ground state energy and double occupancy, the disappearance of the Fermi surface in the $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model, and so on. The method is applicable to any model with on-site repulsion only.Cluster perturbation theory is a technique for calculating the spectral weight of Hubbard models of strongly correlated electrons, which combines exact diagonalizations on small clusters with strong-coupling perturbation theory at leading order. It is exact in both the strong- and weak-coupling limits and provides a good approximation to the spectral function at any wave vector. Following the paper by S\'en\'echal et al. [Phys. Rev. Lett. $84,$ 522 (2000)], we provide a more complete description and derivation of the method. We illustrate some of its capabilities, in particular regarding the effect of doping, the calculation of ground state energy and double occupancy, the disappearance of the Fermi surface in the $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model, and so on. The method is applicable to any model with on-site repulsion only.

arXiv:cond-mat/0205044Physical review. B, Condensed matterAug 30, 2002238 citations

The Strong Coupling Limit of the Hubbard Model

Li Liu, Hong Yao, Steven Allan Kivelson

Bulletin of the American Physical SocietyMar 17, 20100 citations

Temperature-dependent electronic structure and ferromagnetism in the d=∞ Hubbard model studied by a modified perturbation theory

Thomas Wegner, Michael Potthoff, Wolfgang Nolting

The infinite-dimensional Hubbard model is studied by means of a modified perturbation theory. The approach reduces to the iterative perturbation theory for weak coupling. It is exact in the atomic limit and correctly reproduces the dispersions and the weights of the Hubbard bands in the strong-coupling regime for arbitrary fillings. Results are presented for the hypercubic and an fcc-type lattice. For the latter we find ferromagnetic solutions. The filling-dependent Curie temperature is compared with the results of a recent quantum Monte Carlo study.The infinite-dimensional Hubbard model is studied by means of a modified perturbation theory. The approach reduces to the iterative perturbation theory for weak coupling. It is exact in the atomic limit and correctly reproduces the dispersions and the weights of the Hubbard bands in the strong-coupling regime for arbitrary fillings. Results are presented for the hypercubic and an fcc-type lattice. For the latter we find ferromagnetic solutions. The filling-dependent Curie temperature is compared with the results of a recent quantum Monte Carlo study.

arXiv:cond-mat/9712139Physical review. B, Condensed matterMar 15, 199824 citations

Strong-coupling thermodynamics of the Hubbard model

D. Grensing, Heinz Koppe

The European Physical Journal BJun 1, 19765 citations

84,

522 (2000)], we provide a more complete description and derivation of the method. We illustrate some of its capabilities, in particular regarding the effect of doping, the calculation of ground state energy and double occupancy, the disappearance of the Fermi surface in the $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model, and so on. The method is applicable to any model with on-site repulsion only.