  It has been known that the time-dependent Hartree-Fock (TDHF) method, or the
time-dependent density functional theory (TDDFT), fails to describe many-body
quantum tunneling. We overcome this problem by superposing a few time-dependent
Slater determinants with the time-dependent generator coordinate method
(TDGCM). We apply this method to scattering of two $\alpha$ particles in one
dimension, and demonstrate that the TDGCM method yields a finite tunneling
probability even at energies below the Coulomb barrier, at which the tunneling
probability is exactly zero in the TDHF. This is the first case in which a
many-particle tunneling is simulated with a microscopic real-time approach.
