1D half-filled paramagnetic Hubbard model.The Luttinger critical exponents

The electronic system of the 1D Hubbard model is not stable due to Peierls instability; the correlations are strong even for the weak Coulomb interaction. The resulting strongly correlated state without Landau quisi–particle excitations is known as the Luttinger liquid. Critical exponents of a power–law dependence of correlation functions at low energies differ substantially for the Luttinger and Fermi liquids. In this paper we evaluate two critical exponents that define non–trivial behavior of the density of electronic states at low frequences and the momentum distribution of the occupation number nearby $k_F$.