Charge and spin fluctuations in the Hubbard model

This paper reviews the slave-boson representations of the Hubbard model. When both spin and charge fermion degrees of freedom are represented by Bose field, the approach is equivalent at the self-consistent saddle point level to the Guntzwiller approximation (GA). The authors show how the determination of the Lagrange multipliers, introduced to enforce the constraints, involves a Mott-Hubbard gap near half-filling for V > Uc (localization edge). The quantum fluctuations are then considered within a renormalized basis of boson fields (restoring the spin-rotation invariance), which brings out two distinct channels, symmetric and antisymmetric. It is remarkable that both spin and charge fluctuations are obtained at the same level of the gaussian fluctuations, as opposed to the standard 1/N expansion. This provides the microscopic basis for a Fermi liquid theory. Both dynamic effects and extension to finite temperature which were beyond the scope of the variational procedure can now be described by this approach. The physical implications of the model (dynamic correlation functions, T3 LnT term of the specific heat, superfluid instability) are finally considered, all of which reflect the Fermi liquid nature of the system