  Nonlinear transport in the one dimensional Hubbard model at half-filling
under a finite bias voltage is investigated by the adaptive time-dependent
density matrix renormalization group method. For repulsive on-site interaction,
dielectric breakdown of the Mott insulating ground state to a current-carrying
nonequilibrium steady state is clearly observed when the voltage exceeds the
charge gap. It is found that by increasing the voltage further the
current-voltage characteristics are scaled only by the charge gap and the
scaling curve exhibits almost linear dependence on the voltage whose slope is
suppressed by the electron correlation. In the case of attractive interaction
the linear conductance is the perfect one $2e^2/h$ which agrees with the
prediction by the Luttinger liquid theory.
