nLab supersymmetry in fractional quantum Hall systems -- references

Supersymmetry in fractional quantum Hall systems

On hidden/emergent supersymmetry in fractional quantum Hall systems (cf. SuSy between Laughlin and Moore-Read states and for a similar phenomenon cf. also hadron supersymmetry).

The density-wave excitations above the topological ground state of 2D electron gases in fractional quantum Hall systems exhibit an

• effective supergeometry

and in the long-wavelength limit are described by an

• effective supergravity theory.

Effective FQH Supergeometry

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 “magnetoroton” 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, talk video]

• 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”

• 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.”

• Koyena Bose, Ajit C. Balram: Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions, Physical Review B 112 3 (2025) [doi:10.1103/p5sq-kczs, arXiv:2502.02686]

See also:

• Christopher Ting, C. H. Lai: Spinning Braid Group Representation and the Fractional Quantum Hall Effect, Nucl. Phys. B 396 (1993) 429-464 [doi:10.1016/0550-3213(93)90659-D, arXiv:hep-th/9202024]

• Brian P. Dolan: $\mathcal{N}=2$ Supersymmetric Yang-Mills and the Quantum Hall Effect, International Journal of Modern Physics A 21 23/24 (2006) 4807-4822 [arXiv:hep-th/0505138, doi:10.1142/S0217751X06033891, pdf]

• Eran Sagi, Raul A. Santos: Supersymmetry in the Fractional Quantum Hall Regime, Phys. Rev. B 95 205144 (2017) [doi:10.1103/PhysRevB.95.205144, arXiv:1610.07627]

• Jin-Beom Bae, Sungjay Lee, section 5 of: Emergent Supersymmetry on the Edges, SciPost Phys. 11 091 (2021) [doi:10.21468/SciPostPhys.11.5.091, arXiv:2105.02148]

• Ajit C. Balram: SUSY at $\nu = 5/2$, section 3 of: High-energy collective modes in fractional quantum Hall liquids: Rise of the parton, talk at Quantum Information and Quantum Matter 2023, CQTS @ NYU Abu Dhabi (May 2023) [pdf, pdf]

Effective FQH Supergravity

Identification of the long-wavelength limit of the GMP mode and its superpartner with an effective (massive, chiral) graviton and gravitino mode (on momentum space, falling into linear representations of area-preserving diffeomorphisms/$W_\infty$-algebras):

• Bo Yang, Zi-Xiang Hu, Z. Papic, F. Duncan M. Haldane: Model Wavefunctions for the Collective Modes and the Magneto-roton Theory of the Fractional Quantum Hall Effect, Phys. Rev. Lett. 108 (2012) 256807 [doi:10.1103/PhysRevLett.108.256807, arXiv:1201.4165]

• F. Duncan M. Haldane: Majorana Physics, Neutral Fermion modes, and a “Gravitino”, in the Moore-Read Fractional Quantum Hall State, talk at Majorana Physics in Condensed Matter, Ettore Majorana Center, Erice Italy (July 12-18, 2013) $[$pdf]

• F. Duncan M. Haldane: Geometrical Description of the Fractional Quantum Hall Effect, Phys. Rev. Lett. 123 (2019) 146801 [doi:10.1103/PhysRevLett.107.116801, arXiv:1904.12231]

• Shiuan-Fan Liou, F. Duncan M. Haldane, Kun Yang, Edward H. Rezayi: Chiral Gravitons in Fractional Quantum Hall Liquids, Phys. Rev. Lett. 123 146801 (2019) [doi:PhysRevLett.123.146801, arXiv:1904.12231]

  (effective gravitational waves)

• Wang Yuzhu: Graviton Modes in Fractional Quantum Hall Liquids, PhD thesis, Nanyang TU (2023) [hndl:10356/165156, pdf]

• J. Liang et al.: Evidence for chiral graviton modes in fractional quantum Hall liquids, Nature 628 (2024) 78–83 [doi:10.1038/s41586-024-07201-w]

  (experimental detection of the “graviton” mode)

• Ajit C. Balram, G. J. Sreejith, Jainendra K. Jain: Splitting of Girvin-MacDonald-Platzman density wave and the nature of chiral gravitons in fractional quantum Hall effect, Phys. Rev. Lett. 133 (2024) 246605 [doi:10.1103/PhysRevLett.133.246605, arXiv:2406.02730]

• Yuzhu Wang, Bo Yang: Geometric Fluctuation of Conformal Hilbert Spaces and Multiple Graviton Modes in Fractional Quantum Hall Effect, Nat. Commun. 14 2317 (2023) [doi:10.1038/s41467-023-38036-0, arXiv:2201.00020]

  (gravitino on p. 8)

• Hui Liu, Zhao Liu, Emil J. Bergholtz: Non-Abelian Fractional Chern Insulators and Competing States in Flat Moiré Bands, Phys. Rev. Lett. 135 (2025) 106604 [doi:10.1103/43nq-ntqm, arXiv:2405.08887]

  (in fractional quantum anomalous Hall systems)

and explicit embedding of these phenomena into (non-relativistic) supergravity:

• 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]

• Yi-Hsien Du: Chiral Graviton Theory of Fractional Quantum Hall States [arXiv:2509.04408]

  (formulation via area-preserving diffeomorphisms and generalization to non-abelian Read-Rezayi states)