  We consider the effect of contact interaction in a prototypical quantum spin
Hall system of pseudo-spin-1/2 particles. A strong effective magnetic field
with opposite directions for the two spin states restricts two-dimensional
particle motion to the lowest Landau level. While interaction between same-spin
particles leads to incompressible correlated states at fractional filling
factors as known from the fractional quantum Hall effect, these states are
destabilized by interactions between opposite spin particles. Exact results for
two particles with opposite spin reveal a quasi-continuous spectrum of extended
states with a large density of states at low energy. This has implications for
the prospects of realizing the fractional quantum spin Hall effect in
electronic or ultra-cold atom systems. Numerical diagonalization is used to
extend the two-particle results to many bosonic particles and trapped systems.
The interplay between an external trapping potential and spin-dependent
interactions is shown to open up new possibilities for engineering exotic
correlated many-particle states with ultra-cold atoms.
