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arXiv · 2611.00204

The Halperin (111) state as a paired composite-fermion wave function: Two exact finite-size identities on the sphere

Glenn Wagner
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Abstract

Two wavefunctions have previously been proposed to describe the $ν=1/2+1/2$ quantum Hall bilayer: $p$-wave pairing of composite fermions and $s$-wave pairing of composite fermions with anti-composite fermions. We show analytically in the spherical geometry and within the Jain-Kamilla lowest Landau level projection scheme that both of these paired composite fermion wavefunctions exactly reproduce the Halperin (111) state for a specific form of the pairing that we derive. We also find a second wavefunction that is common between both classes of wavefunctions. However, we provide evidence the two variational families generate overlapping but not identical sets of electronic states, ruling out a universal reparametrization that identifies their wavefunctions.

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Glenn Wagner. 2026-10-30. The Halperin (111) state as a paired composite-fermion wave function: Two exact finite-size identities on the sphere. https://arxiv.org/abs/2611.00204

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