Spin- and charge-excitation gaps in the one-dimensional periodic Anderson model

Spin and charge excitations in the one-dimensional periodic Anderson model at half filling are studied in the entire range of the Coulomb interaction U. It is confirmed by exact numerical diagonalization of up to eight sites that an excitation gap exists for any U. In the strong-coupling region, both the spin-excitation gap ${\mathrm{\Delta }}_{\mathit{s}}$ and charge-excitation gap ${\mathrm{\Delta }}_{\mathit{c}}$ decrease with increasing U. A finite-size scaling shows that ${\mathrm{\Delta }}_{\mathit{s}}$ decreases exponentially as a function of U which is consistent with the spin gap in the Kondo-lattice model. The charge gap ${\mathrm{\Delta }}_{\mathit{c}}$ decreases much more slowly than the spin gap. The ratio between the two gaps, R=${\mathrm{\Delta }}_{\mathit{c}}$/${\mathrm{\Delta }}_{\mathit{s}}$, increases monotonically from unity and diverges in the strong-coupling limit: it appears to be a useful quantity for measuring the strength of electron correlation in a Kondo insulator.