Equation of motion approach for the Hubbard model: improved decoupling   scheme, charge fluctuations, and the metal-insulator transition
  A new decoupling scheme is developed for the Hubbard model which provides a unified description of the spin-symmetric (paramagnetic metallic and insulating) phases as well as the broken-symmetry AFI phase. Independent of magnetic ordering, the scheme yields, in the lowest order, the correct strong-coupling bandwidth of order J (for the NN hopping model) and band gap of order U, a non-zero critical interaction strength (above which the band gap opens) only if same sublattice hopping (e.g., NNN hopping) is also present, and the correct integrated spectral weights (1/2 per spin) in each band for the half-filled model. The effects of charge and spin fluctuations, including spin twisting due to finite spin correlation length, are investigated with a static, random approximation. A self-consistent evaluation of the disorder-averaged self energy within the CPA is carried out numerically. Fluctuations activate the hopping term at first order resulting in band broadening, and the consequent decrease in the band gap with fluctuation strength is obtained for several U values in two and three dimensions. We find that the band gap shrinks to zero continuously, and subsequently the density of states N(0) between the bands grows continuously, leading to a continuous metal-insulator transition. For finite doping there is transfer of spectral weight between the Hubbard bands, and a qualitative change in the nature of the quasiparticle band dispersion, with an effective doping-induced hopping strength and bandwidth of order xt. 
Avinash Singh