Numerical evidence of anyonic exciton superfluidity in ν=1/3+1/3 quantum Hall bilayers

Bilayer quantum Hall systems can host exciton superfluidity, exemplified by the Halperin (111) state. Recent transport at ν=1/3+1/3 in bilayer graphene shows a singularity versus interlayer spacing and nearly quantized Coulomb drag, indicating neutral interlayer exciton pairing. Field theory predicts a continuous (112)→(330) transition described by QED₃-Chern-Simons and an anyonic exciton superfluid under slight pseudospin doping. Motivated by these results, we perform large-scale iDMRG at ν=1/3+1/3. Neutral pseudospin doping yields a finite-momentum exciton condensate with algebraic correlations. At zero doping, increasing spacing drives a weakly first-order (112)→(330) transition with emergent Dirac cones and C₂ anisotropy; with doping, a CDW competes with—and can supplant—the condensate at larger spacing or when pinning is favored. These numerical predictions are directly testable in bilayer Laughlin devices.