Abstract
We consider the Hubbard model on the Bethe lattice with infinite Coordination number and construct (i) a systematic series of self-consistent approximations to the one-particle Green's function, G(n)(ω), n = 2,3,... and (ii) conduct an exact diagonalization study of the Hubbard star and the star of the stars. We present analytic and numerical results for the Mott-Hubbard transition at half filling. We find consistently (i) a critical Uc ∼ 2.5 and (ii) that the gap opens like ∼(U-Uc)3/2.
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