Wave Function and Emergent SU(2) Symmetry in ${\nu }_T=1$ Quantum Hall Bilayer

Abstract

We propose a trial wave function for the quantum Hall bilayer system of total filling factor ${\nu }_T=1$ at a layer distance $d$ to magnetic length $\ell$ ratio $d/\ell ={\kappa }_{c1}\approx 1.1$, 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 nature of these excitons indicating an emergent SU(2) symmetry for the composite bosons at $d/\ell ={\kappa }_{c1}$, 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 $d/\ell ={\kappa }_{c1}$, which supports our theory.

4+8 pages, 2+3 figures

References in corpus (4)

• Paired composite fermion phase of quantum Hall bilayers at ν= 1/2 + 1/2
• Trial Wavefunctions for ν= 1/2 + 1/2 Quantum Hall Bilayers
• Numerical Study of Quantum Hall Bilayers at Total Filling ${\nu }_T=1$: A New Phase at Intermediate Layer Distances
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• Exciton Condensation in Quantum Hall Bilayers at Total Filling ${\nu }_T=5$
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• Successive electron-vortex binding in quantum Hall bilayers at $\nu =\frac{1}{4}+\frac{3}{4}$
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• On dualities of paired quantum Hall bilayer states at ${\nu }_T=\frac{1}{2}+\frac{1}{2}$