The Hubbard Model and Its Application to Conjugated π-Electron Systems
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When the inventors of the Hubbard model (Anderson, 1959; Hubbard, 1963; Gutzwiller, 1963; Kanamori 1963) proposed their simplified one-band Hamiltonian with only on-site interaction, they had in mind the d electrons in transition metals. More recently, the Hubbard model has been also advocated in the context of high-temperature superconductors (Anderson, 1988). However, it is a priori not obvious why a one-band model should be able to describe transition metal compounds with partly degenerate d bands, often hybridized with s and p states, and, in fact, there are examples where a single-band model fails to capture some important aspects (Kanamori, 1990). This question has been extensively discussed for the layered copper oxides. Several calculations indicate that in this case the one-band Hubbard model or the related t — J model do describe the low-lying charge and spin excitations (Zhang and Rice, 1988; Luo and Bickers, 1993), but the detailed mapping appears to be rather complicated (Meinders et al., 1993).
KeywordsHubbard Model Wannier Function Double Occupancy Extended Hubbard Model Layered Copper Oxide
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