Coulomb, orbital, and spin interactions in 1D exactly solved model

Abstract
Large number of actual heavy-fermionic alloys display non-Fermi liquid behavior [l]. Recent achievements in the description of 1D models give the possibility to indicate some mechanisms of forming special properties of fermionic systems. Usual parameters of these models are Coulomb, orbital, and spin interaction. An 1D integrable model of the Hubbard's chain of the electrons with the model orbital interaction is presented. Exact solutions were obtained for different scattering channels of the electrons, namely the spin and orbital one. The preferable channel of the scattering was determined by means of numerical calculations and comparison of the energy levels of each scattering channel. The dependence of the scattering matrix on the parameters of Coulomb, orbital, and spin interactions gives the possibility to present the properties of the considered system in different ranges of these parameters and to determine the values of parameters which correspond to the electron coupling.