Abstract
The existence of antiferromagnetism is investigated in the single-band Hubbard Hamiltonian in the limit of bandwidth much less than intra-atomic Coulomb interaction of electrons. We make use of the canonical transformation and ``spectral decomposition'' of the electron creation operators proposed by Harris and Lange, to write down a Green's function which describes electrons in the lower of the split bands of Hubbard's solution. The equation of motion is solved using the moment-conserving decoupling approximation of Tahir-Kheli and Jarrett [R. Tahir-Kheli and H. S. Jarrett, Phys. Rev. 180, 544 (1968)]. We find within our approximation that it is impossible to have an antiferromagnetic state for other than one electron per site. To remedy this defect of the single-band model we investigate a simplified two-band model in the limit of intra-atomic Coulomb and exchange interaction much greater than the bandwidth, and find that antiferromagnetism is possible for the two nearly half-filled bands. We also discuss effects of the antiferromagnetic ordering on the conductivity in our simplified model, and discuss applicability of the theory to real transition metals and transition-metal oxides.
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