Spin and charge gaps in the one-dimensional Kondo-lattice model with   Coulomb interaction between conduction electrons
  The density-matrix renormalization-group method is applied to the one-dimensional Kondo-lattice model with the Coulomb interaction between the conduction electrons. The spin and charge gaps are calculated as a function of the exchange constant $J$ and the Coulomb interaction $U_c$. It is shown that both the spin and charge gaps increase with increasing $J$ and $U_c$. The spin gap vanishes in the limit of $J \rightarrow 0$ for any $U_c$ with an exponential form, $\Delta_s\propto \exp{[-1/\alpha (U_c) J \rho]}$. The exponent, $\alpha (U_c)$, is determined as a function of $U_c$. The charge gap is generally much larger than the spin gap. In the limit of $J \rightarrow 0$, the charge gap vanishes as $\Delta_c=\frac{1}{2}J$ for $U_c=0$ but for a finite $U_c$ it tends to a finite value, which is the charge gap of the Hubbard model. 
N. Shibata, T. Nishino, K. Ueda, and C. Ishii