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arXiv · 2503.22940

Mapping the Second Landau Level PH-Pfaffian State to the Lowest Landau Level

Jian Yang
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Abstract

Recently we proposed a state described by the second Landau level (SLL) projection of the antiholomorphic Pfaffian wavefunction as a candidate for the ground state of the 5/2 fractional quantum Hall effect. In this paper we provide a mathematical proof that, when mapped to the lowest Landau level (LLL), the aforementioned state, which we call the SLL PH-Pfaffian state, becomes exactly a LLL projected orbital angular momentum l = -3 pairing Pfaffian state, which we call the LLL antiholomorphic f-wave pairing Pfaffian state, or the LLL af-Pfaffian state for short. We further prove that there is also an exact mapping between the upstream neutral Majorana fermion edge mode of the SLL PH-Pfaffian state and that of the LLL af-Pfaffian state. However, we find that while there exists an upstream neutral boson edge mode in the LLL af-Pfaffian state, it has no mapped counterpart in the SLL PH-Pfaffian state.

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Jian Yang. 2025-03-29. Mapping the Second Landau Level PH-Pfaffian State to the Lowest Landau Level. https://arxiv.org/abs/2503.22940

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