nLab supersymmetry in fractional quantum Hall systems -- references

Supersymmetry in fractional quantum Hall systems

On hidden/emergent supersymmetry in fractional quantum Hall systems.

(for a similar phenomenon cf. also hadron supersymmetry)

The use of supergeometry in the description of fractional quantum Hall systems, and the observation that the Moore-Read state is the top super field-component of a super-Laughlin wavefunction (see there) was promoted in:

Kazuki Hasebe: Supersymmetric Quantum-Hall Effect on a Fuzzy Supersphere, Phys. Rev. Lett. 94 (2005) 206802 [doi:10.1103/PhysRevLett.94.206802]
Kazuki Hasebe: Quantum Hall liquid on a noncommutative superplane, Phys. Rev. D 72 (2005) 105017 [doi:10.1103/PhysRevD.72.105017]
Kazuki Hasebe: Quantum Hall Effect Based on SUSY Non-Commutative Geometry, Progress of Theoretical Physics Supplement 171 (2007) 154–159 [doi:10.1143/PTPS.171.154]
Kazuki Hasebe: Unification of Laughlin and Moore–Read states in SUSY quantum Hall effect, Physics Letters A 372 9 (2008) 1516-1520 [doi:10.1016/j.physleta.2007.09.071]
Kazuki Hasebe: Supersymmetric Quantum Hall Liquid with a Deformed Supersymmetry, Phys. Atom. Nucl. 73 (2010) 345-351 [arXiv:0901.1724, doi:10.1134/S1063778810020225]
Kazuki Hasebe: Supersymmetric Quantum Spin Model and Quantum Hall Effect, Soryushiron Kenkyu Electronics 117 6 (2010) F59- [doi:10.24532/soken.117.6_F59, spire:1687527]

Based on this, the proposal that also the “magentoroton” and the “neutral fermion” excitations of the $\nu = 5/2$ Moore&Read-state should be superpartners of each other, is due to:

Andrey Gromov, Emil J. Martinec, Shinsei Ryu: Collective excitations at filling factor $5/2$ : The view from superspace, Phys. Rev. Lett. 125 (2020) 077601 [doi:10.1103/PhysRevLett.125.077601, arXiv:1909.06384]

(via superspace formulation)

further discussed in:

Ken K. W. Ma, Ruojun Wang, Kun Yang: Realization of Supersymmetry and Its Spontaneous Breaking in Quantum Hall Edges, Phys. Rev. Lett. 126 (2021) 206801 [doi:10.1103/PhysRevLett.126.206801, arXiv:2101.05448]
Patricio Salgado-Rebolledo, Giandomenico Palumbo: Nonrelativistic supergeometry in the Moore-Read fractional quantum Hall state, Phys. Rev. D 106 (2022) 065020 [doi:10.1103/PhysRevD.106.065020, arXiv:2112.14339]
Songyang Pu, Ajit C. Balram, Mikael Fremling, Andrey Gromov, Zlatko Papić: Signatures of Supersymmetry in the $\nu = 5/2$ Fractional Quantum Hall Effect, Phys. Rev. Lett. 130 (2023) 176501 [doi:10.1103/PhysRevLett.130.176501, arXiv:2301.04169]

“Our results suggest that the SUSY structure is intrinsically present in spectral properties of the $\nu = 5/2$ state”
Dung Xuan Nguyen, Kartik Prabhu, Ajit C. Balram, Andrey Gromov: Supergravity model of the Haldane-Rezayi fractional quantum Hall state, Phys. Rev. B 107 (2023) 125119 [doi:10.1103/PhysRevB.107.125119, arXiv:2212.00686]

(proposal for a supergravity formulation)
Yang Liu, Tongzhou Zhao, T. Xiang: Resolving Geometric Excitations of Fractional Quantum Hall States, Phys. Rev. B 110 195137 (2024) [arXiv:2406.11195, doi:10.1103/PhysRevB.110.195137]

“Our findings support the hypothesis of emergent supersymmetry and highlight the potential for detecting neutral fermions in future experiments.”