Wave Function and Emergent SU(2) Symmetry in the νT=1 Quantum Hall Bilayer

Biao Lian, Shou-Cheng Zhang
2018 Physical Review Letters  
We propose a trial wave function for the quantum Hall bilayer system of total filling factor ν_T=1 at a layer distance d to magnetic length ℓ ratio d/ℓ=κ_c1≈1.1, where the lowest charged excitation is known to have a level crossing. The wave function has two-particle correlations which fit well with those in previous numerical studies, and can be viewed as a Bose-Einstein condensate of free excitons formed by composite bosons and anti-composite bosons in different layers. We show the free
more » ... of these excitons indicating an emergent SU(2) symmetry for the composite bosons at d/ℓ=κ_c1, which leads to the level crossing in low-lying charged excitations. We further show the overlap between the trial wave function and the ground state of a small size exact diagonalization is peaked near d/ℓ=κ_c1, which supports our theory.
doi:10.1103/physrevlett.120.077601 pmid:29542942 fatcat:r6ufi7clnbctberr6qugot6ah4