Gutzwiller wave-function description of a particle in a fermionic bath

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Abstract
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 (≃1/ρ) for small densities ρ; in the Gutzwiller approach it scales with ρ, 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 ρ≲0.6.