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We study the phase diagram of quantum Hall bilayer systems with total filing$\nu_T=1/2+1/2$ of the lowest Landau level as a function of layer distances$d$. Based on numerical exact diagonalization calculations, we obtain threedistinct phases, including an exciton superfluid phase with spontaneousinterlayer coherence at small $d$, a composite Fermi liquid at large $d$, andan intermediate phase for $1.1<d/l_B<1.8$ ($l_B$ is the magnetic length). Thetransition from the exciton superfluid to the intermediate phase is identifiedby (i) a dramatic change in the Berry curvature of the ground state undertwisted boundary conditions on the two layers; (ii) an energy level crossing ofthe first excited state. The transition from the intermediate phase to thecomposite Fermi liquid is identified by the vanishing of the exciton superfluidstiffness. Furthermore, from our finite-size study, the energy cost oftransferring one electron between the layers shows an even-odd effect andpossibly extrapolates to a finite value in the thermodynamic limit, indicatingthe enhanced intralayer correlation. Our identification of an intermediatephase and its distinctive features shed new light on the theoreticalunderstanding of the quantum Hall bilayer system at total filling $\nu_T=1$.

Numerical Study of Quantum Hall Bilayers at Total Filling $\nu_T=1$: A New Phase at Intermediate Layer Distances