Spin-rotation-invariant slave-boson approach to the Hubbard model

We present a slave-boson representation for the Hubbard model, introducing Bose fields for the empty, singly, and doubly occupied sites and show that the boson for the singly occupied site must transform as a tensor of rank two under spin rotations. This generalizes the formulation of Kotliar and Ruckenstein, which is not manifestly spin-rotation invariant. The paramagnetic saddle point of the corresponding functional integral is identical to Gutzwiller’s solution. As an illustration of the method, we calculate the $T^3$lnT spin-fluctuation contribution to the specific heat and find it to be fully consistent with Fermi-liquid theory. We discuss further applications of this approach.