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Cluster Approximation and Perturbation Theory for Band Models with Coulomb Interaction
Author(s) -
Lorenz B.
Publication year - 1981
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221080216
Subject(s) - coulomb , hubbard model , perturbation (astronomy) , physics , perturbation theory (quantum mechanics) , fermion , cluster (spacecraft) , quantum electrodynamics , mean field theory , quantum mechanics , mathematical physics , electron , superconductivity , computer science , programming language
Band models with intrasite (Hubbard) and intersite Coulomb interactions are treated in a cluster approximation taking into account the interactions and the transfer within clusters of sites rigorously. Between different clusters the interaction is decoupled in a mean field approximation and the transfer term is treated as a perturbation. The ground‐state energy of the one‐dimensional Hubbard model is calculated up to fourth order in the perturbation and is compared with other approximations and the exact result. In the one‐dimensional spinless fermion model the perturbation is treated without further approximations by solving Dyson's equation for the one‐particle Green's function. The order‐disorder transition in this model is discussed.