QUASI-PARTICLES IN 2-DIMENSIONAL HUBBARD-MODEL - SPLITTING OF SPECTRAL WEIGHT

It is shown that the energy (epsilon) and momentum (k) dependences of the electron self-energy function Sigma(k, epsilon+i0)=Sigma(R)(k, epsilon) in two-dimension are Im Sigma(R)(k, epsilon)=-a epsilon(2)\epsilon-xi(k)\(-y(k)), where a is some constant, xi(k)=epsilon(k)-mu, epsilon(k) being the band energy, and the critical exponent gamma(k), which depends on the curvature of the Fermi surface at k, satisfies 0 less than or equal to gamma(k) less than or equal to 1. This leads to a new type of electron liquid, which is the Fermi liquid in the limit of epsilon, xi(k) --> 0 but for xi(k) not equal 0 has a split one-particle spectra, as in the Tomonaga-Luttinger liquid.