  Using the time-dependent density-matrix renormalization group (tDMRG), we
study the time evolution of electron wave packets in one-dimensional (1D)
metal-superconductor heterostructures. The results show Andreev reflection at
the interface, as expected. By combining these results with the well-known
single-spin-species electron-hole transformation in the Hubbard model, we
predict an analogous spin Andreev reflection in metal-Mott insulator
heterostructures. This effect is numerically confirmed using 1D tDMRG, but it
is expected to be present also in higher dimensions, as well as in more general
Hamiltonians. We present an intuitive picture of the spin reflection, analogous
to that of Andreev reflection at metal-superconductors interfaces. This allows
us to discuss a novel antiferromagnetic proximity effect. Possible experimental
realizations are discussed.
