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

2017/07/31 by Biao Lian, Shou-Cheng Zhang
Mathematics · Physics and Astronomy · #Boson #Exciton #Function (biology) #Geometry #Identical particles #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Semiconductor Quantum Structures and Devices #Symmetry (geometry) #Wave function #cond-mat.mes-hall #cond-mat.str-el

paper · pdf · doi:10.1103/physrevlett.120.077601

published as Phys. Rev. Lett. 120, 077601 (2018) · 4+8 pages, 2+3 figures

openalex created_date 2017/07/14 · arxiv created 2017/10/17 · openalex publication_date 2018/02/16 · arxiv updated 2018/02/21 · openalex updated_date 2026/08/06

Abstract

We propose a trial wave function for the quantum Hall bilayer system of total filling factor \ensuremathν_T=1 at a layer distance d to magnetic length \ensuremathℓ ratio d/\ensuremathℓ=\ensuremathκ_c1\ensuremath≈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 anticomposite bosons in different layers. We show the free nature of these excitons indicating an emergent SU(2) symmetry for the composite bosons at d/\ensuremathℓ=\ensuremathκ_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/\ensuremathℓ=\ensuremathκ_c1, which supports our theory.

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