  The quantum Hall effect is usually observed when the two-dimensional electron
gas is subjected to an external magnetic field, so that their quantum states
form Landau levels. In this work we predict that a new phenomenon, the quantum
anomalous Hall effect, can be realized in Hg$_{1-y}$Mn$_{y}$Te quantum wells,
without the external magnetic field and the associated Landau levels. This
effect arises purely from the spin polarization of the $Mn$ atoms, and the
quantized Hall conductance is predicted for a range of quantum well thickness
and the concentration of the $Mn$ atoms. This effect enables dissipationless
charge current in spintronics devices.
