Global phase diagram of two-component Bose gases in antiparallel magnetic fields

We study the ground-state phase diagram of two-dimensional two-component (or pseudospin-1/2) Bose gases in mutually antiparallel synthetic magnetic fields in the space of the total filling factor and the ratio of the intercomponent coupling g up down arrow to the intracomponent coupling g > 0. This time-reversal-invariant setting represents a bosonic analog of spin Hall systems. Using exact diagonalization, we find that (fractional) quantum spin Hall states composed of a pair of nearly independent quantum Hall states are remarkably robust and persist for g up down arrow up to as large as g. For g up down arrow = -g, we find the exact many-body ground state in which particles in different spin states form pairs. This gives the exact critical line beyond which the system collapses in the thermodynamic limit.