  We study interaction effect of quantum spin Hall state in InAs/GaSb quantum
wells under an in-plane magnetic field by using the self-consistent mean field
theory. We construct a phase diagram as a function of intra-layer and
inter-layer interactions, and identify two novel phases, a charge/spin density
wave phase and an exciton condensate phase. The charge/spin density wave phase
is topologically non-trivial with helical edge transport at the boundary, while
the exciton condensate phase is topologically trivial. The Zeeman effect is
strongly renormalized due to interaction in certain parameter regimes of the
system, leading to a much smaller g-factor, which may stabilize the helical
edge transport.
