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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{wagner2026halperin,
  title = {{The Halperin (111) state as a paired composite-fermion wave function: Two exact finite-size identities on the sphere}},
  author = {Glenn Wagner},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00204},
  eprint = {2611.00204},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00204},
}
RIS
TY  - UNPB
TI  - The Halperin (111) state as a paired composite-fermion wave function: Two exact finite-size identities on the sphere
AU  - Glenn Wagner
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00204
UR  - https://arxiv.org/abs/2611.00204
AB  - 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.
ER  -