Signatures of emergent supersymmetry in the ν=5/2 fractional quantum Hall effect*

The Moore-Read Pfaffian state has two low-lying neutral excitations, a magnetoroton mode and a neutral fermion mode. Recently, Gromov, Martinec, and Ryu proposed a theory which formulated the two modes as supersymmetric partners of each other [1]. Inspired by their work, we construct wave functions for the two modes in different closed geometries. We evaluate the variational energies of the two wave functions in large system sizes and find signatures of supersymmetry for an interaction in the vicinity of the second Landau level Coulomb point. We also compare the constructions of the neutral excitation modes from previous approaches and find they give identical description in the long-wavelength limit. 

[1] A. Gromov, E. J. Martinec, and S. Ryu, Phys. Rev. Lett. 125, 077601 (2020).