We develop a nonperturbative bosonization approach for bilayer quantum Hall systems at nu(T)=1, which allows us to systematically study the existence of an exciton condensate in these systems. An effective boson model is derived and the excitation spectrum is calculated in both the Bogoliubov and the Popov approximations. In the latter case, we show that the ground state of the system is an exciton condensate only when the distance between the layers is very small compared to the magnetic length, indicating that the system possibly undergoes another phase transition before the incompressible-compressible one. The effect of a finite electron interlayer tunneling is included and a quantitative phase diagram is proposed.
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