Quasi-Particles in Two-Dimensional Hubbard Model: Splitting of Spectral Weight

It is shown that the energy (ε) and momentum (k) dependences of the electron selfenergy function Σ(k, ε + i0) ≡ Σ(k, ε) are, ImΣ(k, ε) = −aε|ε − ξk| −γ(k) where a is some constant, ξk = ε(k)−μ, ε(k) being the band energy, and the critical exponent γ(k), which depends on the curvature of the Fermi surface at k, satisfies, 0 ≤ γ(k) ≤ 1. This leads to a new type of electron liquid, which is the Fermi liquid in the limit of ε, ξk → 0 but for ξk 6= 0 has a split one-particle spectra as in the Tomonaga-Luttinger liquid. (submitted to J. Phys. Soc. Japan: [Letter])