GUTZWILLER WAVE-FUNCTION DESCRIPTION OF A PARTICLE IN A FERMIONIC BATH

We study the energy and effective mass of a moving down spin interacting with a bath of up spins using an extended Gutzwiller wave function. In the Bethe-ansatz solution in one dimension the effective mass scales with the density of states at the Fermi level (congruent-to 1/p) for small densities p; in the Gutzwiller approach it scales with p, which shows the inadequacy to reproduce the correct low-energy behavior. From the energy we obtain the instability of the fully polarized state (for infinite repulsive interaction) at a density p less-than-or-similar-to 0.6.