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We consider the effect of contact interaction in a prototypical quantum spinHall system of pseudo-spin-1/2 particles. A strong effective magnetic fieldwith opposite directions for the two spin states restricts two-dimensionalparticle motion to the lowest Landau level. While interaction between same-spinparticles leads to incompressible correlated states at fractional fillingfactors as known from the fractional quantum Hall effect, these states aredestabilized by interactions between opposite spin particles. Exact results fortwo particles with opposite spin reveal a quasi-continuous spectrum of extendedstates with a large density of states at low energy. This has implications forthe prospects of realizing the fractional quantum spin Hall effect inelectronic or ultra-cold atom systems. Numerical diagonalization is used toextend the two-particle results to many bosonic particles and trapped systems.The interplay between an external trapping potential and spin-dependentinteractions is shown to open up new possibilities for engineering exoticcorrelated many-particle states with ultra-cold atoms.

Fragility of the fractional quantum spin Hall effect in quantum gases