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 $J\to 0$ for any $U_c$ with an exponential form, ${\Delta }_s\propto \exp [-\frac{1}{\alpha \left(U_c\right)J\rho }]$. The exponent, $\alpha \left(U_c\right)$, is determined as a function of $U_c$. The charge gap is generally much larger than the spin gap. In the limit of $J\to 0$, the charge gap vanishes as ${\Delta }_c=\frac{1}{2}J$ for $U_c=0\mathrm{}$ but for a finite $U_c$ it tends to a finite value, which is the charge gap of the Hubbard model.