  The quintessential two-dimensional lattice model that describes the
competition between the kinetic energy of electrons and their short-range
repulsive interactions is the repulsive Hubbard model. We study a time-reversal
symmetric variant of the repulsive Hubbard model defined on a planar lattice:
Whereas the interaction is unchanged, any fully occupied band supports a
quantized spin Hall effect. We show that at 1/2 filling of this band, the
ground state develops spontaneously and simultaneously Ising ferromagnetic
long-range order and a quantized charge Hall effect when the interaction is
sufficiently strong. We ponder on the possible practical applications, beyond
metrology, that the quantized charge Hall effect might have if it could be
realized at high temperatures and without external magnetic fields in strongly
correlated materials.
