  The existence of conserved spin Hall currents is shown in a strongly
correlated system without involving spin-orbit coupling. The spin Hall
conductivity is determined by intrinsic bulk properties, which remains finite
even when the charge resistivity diverges in strong magnetic fields at zero
temperature. The state in the latter limit corresponds to a spin Hall
insulator. Such a system is a doped Mott insulator described by the phase
string theory, and spin Hall effect is predicted to coexist with the Nernst
effect to characterize the intrinsic properties of the low-temperature
pseudogap phase. Possible applications in spintronics are also mentioned.
