Perturbation Theory and Singularities in Two-Dimensionai Hubbard Model at Low Electron Density

The two-dimensional Hubbard model has been studied in the region of low electron density based on the t-matrix approximation. This can take proper account of the singular behaviors of the forward scattering whose importance was indicated by Anderson. By performing first the angular integrations in the irreducible particle-particle correlation function, we can prove analytically that all of the poles of the t-matrix lie on the real axis. Hence the t-matrix and then the self-energy of the retarded Green function, σ (k, z), are analytic in the upper half-plane of the energy variable, z. This, together with Im σ (kF, ∊ + i δ)∝∊s2 In |∊|, leads to the conclusion that the electrons described by the two-dimensional Hubbard model are Fermi liquid, at least in the region of low electron density.