nLab supersymmetry in fractional quantum Hall systems -- references

Supersymmetry in fractional quantum Hall systems

On hidden supersymmetry in fractional quantum Hall systems between even- and odd-level (filling-fraction) quantum states (Laughlin wavefunctions and their variants):

(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 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 specifically the two collective modes 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 (2012) 206801 [doi:10.1103/PhysRevLett.126.206801, arXiv:2101.05448]

• 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]

  (supergravity formulation)