Fermi-liquid theory in the low-density two-dimensional Hubbard model

We examine the validity of Fermi-liquid theory in the low-density two-dimensional Hubbard model. From the ground-state energy we obtain the quasiparticle energy and the Landau interaction function. Then we prove that the quasiparticle-interaction function is finite and that the quasiparticle residue is nonzero for repulsive interactions. We also find, as a function of the excitation energy ε, that the quasiparticle lifetime ∼1/ ε2lnε. Hence, we conclude that Fermi-liquid theory holds in our model.