@article{Laughlin,
  author  = {Laughlin, Robert B.},
  title   = {Anomalous quantum {Hall} effect: an incompressible quantum fluid with fractionally charged excitations},
  journal = {Physical Review Letters},
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  doi     = {10.1103/PhysRevLett.50.1395},
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}

@article{Haldane,
  author  = {Haldane, F. D. M.},
  title   = {Fractional quantization of the {Hall} effect: a hierarchy of incompressible quantum fluid states},
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  number  = {7},
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  note    = {\href{https://doi.org/10.1103/PhysRevLett.51.605}{doi:10.1103/PhysRevLett.51.605}},
  doi     = {10.1103/PhysRevLett.51.605},
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}

@article{Rougerie,
  author  = {Rougerie, Nicolas},
  title   = {On the {Laughlin} function and its perturbations},
  journal = {S{\'e}minaire Laurent Schwartz --- EDP et applications},
  year    = {2018--2019},
  pages   = {1--17},
  note    = {Exp.~II. \href{https://doi.org/10.5802/slsedp.131}{doi:10.5802/slsedp.131}},
  doi     = {10.5802/slsedp.131},
  url     = {https://doi.org/10.5802/slsedp.131},
  eprint  = {1906.11656},
  archivePrefix = {arXiv}
}

@article{NWY,
  author  = {Nachtergaele, Bruno and Warzel, Simone and Young, Amanda},
  title   = {Spectral gaps and incompressibility in a {$\nu=1/3$} fractional quantum {Hall} system},
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  volume  = {383},
  pages   = {1093--1149},
  year    = {2021},
  note    = {\href{https://doi.org/10.1007/s00220-021-03997-0}{doi:10.1007/s00220-021-03997-0}},
  doi     = {10.1007/s00220-021-03997-0},
  url     = {https://doi.org/10.1007/s00220-021-03997-0},
  eprint  = {2004.04992},
  archivePrefix = {arXiv}
}

@article{WY,
  author  = {Warzel, Simone and Young, Amanda},
  title   = {The spectral gap of a fractional quantum {Hall} system on a thin torus},
  journal = {Journal of Mathematical Physics},
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  number  = {4},
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  note    = {\href{https://doi.org/10.1063/5.0084677}{doi:10.1063/5.0084677}},
  doi     = {10.1063/5.0084677},
  url     = {https://doi.org/10.1063/5.0084677},
  eprint  = {2112.13764},
  archivePrefix = {arXiv}
}

@article{Knabe,
  author  = {Knabe, Stefan},
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  note    = {\href{https://doi.org/10.1007/BF01019721}{doi:10.1007/BF01019721}},
  doi     = {10.1007/BF01019721},
  url     = {https://doi.org/10.1007/BF01019721}
}

@article{Cruz,
  author  = {Cruz, Esther and Baccari, Flavio and Tura, Jordi and Schuch, Norbert and Cirac, J. Ignacio},
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  volume  = {4},
  pages   = {023161},
  year    = {2022},
  note    = {\href{https://doi.org/10.1103/PhysRevResearch.4.023161}{doi:10.1103/PhysRevResearch.4.023161}},
  doi     = {10.1103/PhysRevResearch.4.023161},
  url     = {https://doi.org/10.1103/PhysRevResearch.4.023161},
  eprint  = {2105.06866},
  archivePrefix = {arXiv}
}

@article{Rai,
  author  = {Rai, Kshiti Sneh and Kull, Ilya and Emonts, Patrick and Tura, Jordi and Schuch, Norbert and Baccari, Flavio},
  title   = {A hierarchy of spectral gap certificates for frustration-free spin systems},
  journal = {Quantum},
  volume  = {10},
  pages   = {2065},
  year    = {2026},
  note    = {\href{https://doi.org/10.22331/q-2026-04-13-2065}{doi:10.22331/q-2026-04-13-2065}},
  doi     = {10.22331/q-2026-04-13-2065},
  url     = {https://doi.org/10.22331/q-2026-04-13-2065},
  eprint  = {2411.03680},
  archivePrefix = {arXiv}
}

@article{TrugmanKivelson1985,
  author = {Trugman, S. A. and Kivelson, S.},
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}

@article{HaldaneRezayi1985FiniteSize,
  author = {Haldane, F. D. M. and Rezayi, E. H.},
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}

@article{GMP,
  author = {Girvin, S. M. and MacDonald, A. H. and Platzman, P. M.},
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@article{LRYRigidity,
  author = {Lieb, Elliott H. and Rougerie, Nicolas and Yngvason, Jakob},
  title = {Rigidity of the {Laughlin} Liquid},
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  doi = {10.1007/s10955-018-2082-1},
  url = {https://doi.org/10.1007/s10955-018-2082-1},
  eprint = {1609.03818},
  archivePrefix = {arXiv},
  note = {\href{https://doi.org/10.1007/s10955-018-2082-1}{doi:10.1007/s10955-018-2082-1}}
}

@article{ChenSeidel2015,
  author = {Chen, Li and Seidel, Alexander},
  title = {Algebraic approach to the study of zero modes of {Haldane} pseudopotentials},
  journal = {Physical Review B}, volume = {91}, pages = {085103}, year = {2015},
  doi = {10.1103/PhysRevB.91.085103},
  eprint = {1409.3569}, archivePrefix = {arXiv}, primaryClass = {cond-mat.str-el},
  note = {\href{https://doi.org/10.1103/PhysRevB.91.085103}{doi:10.1103/PhysRevB.91.085103}}
}

@article{MazaheriOrtizNussinovSeidel2015,
  author = {Mazaheri, Tahereh and Ortiz, Gerardo and Nussinov, Zohar and Seidel, Alexander},
  title = {Zero modes, bosonization, and topological quantum order: The {Laughlin} state in second quantization},
  journal = {Physical Review B}, volume = {91}, pages = {085115}, year = {2015},
  doi = {10.1103/PhysRevB.91.085115},
  eprint = {1409.3577}, archivePrefix = {arXiv}, primaryClass = {cond-mat.str-el},
  note = {\href{https://doi.org/10.1103/PhysRevB.91.085115}{doi:10.1103/PhysRevB.91.085115}}
}

@article{NakamuraWangBergholtz2012,
  author = {Nakamura, Masaaki and Wang, Zheng-Yuan and Bergholtz, Emil J.},
  title = {Exactly Solvable Fermion Chain Describing a {$\nu=1/3$} Fractional Quantum {Hall} State},
  journal = {Physical Review Letters}, volume = {109}, number = {1},
  pages = {016401}, year = {2012}, doi = {10.1103/PhysRevLett.109.016401},
  eprint = {1110.5033}, archivePrefix = {arXiv},
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  note = {\href{https://doi.org/10.1103/PhysRevLett.109.016401}{doi:10.1103/PhysRevLett.109.016401}}
}

@article{WangNakamura2013,
  author = {Wang, Zheng-Yuan and Nakamura, Masaaki},
  title = {One-dimensional lattice model with an exact matrix-product ground state describing the {Laughlin} wave function},
  journal = {Physical Review B}, volume = {87},
  pages = {245119}, year = {2013}, doi = {10.1103/PhysRevB.87.245119},
  eprint = {1206.3071}, archivePrefix = {arXiv},
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  note = {\href{https://doi.org/10.1103/PhysRevB.87.245119}{doi:10.1103/PhysRevB.87.245119}}
}

@article{Jansen2012,
  author = {Jansen, Sabine},
  title = {Fermionic and bosonic {Laughlin} state on thick cylinders},
  journal = {Journal of Mathematical Physics}, volume = {53},
  pages = {123306}, year = {2012}, doi = {10.1063/1.4768250},
  eprint = {1109.4022}, archivePrefix = {arXiv},
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  note = {\href{https://doi.org/10.1063/1.4768250}{doi:10.1063/1.4768250}}
}

@article{WarzelYoung2023BulkEdge,
  author = {Warzel, Simone and Young, Amanda},
  title = {A Bulk Spectral Gap in the Presence of Edge States for a Truncated Pseudopotential},
  journal = {Annales Henri Poincar\'e}, volume = {24},
  pages = {133--178}, year = {2023}, doi = {10.1007/s00023-022-01210-z},
  eprint = {2108.10794}, archivePrefix = {arXiv},
  url = {https://doi.org/10.1007/s00023-022-01210-z},
  note = {\href{https://doi.org/10.1007/s00023-022-01210-z}{doi:10.1007/s00023-022-01210-z}}
}

@article{LemmNachtergaeleWarzelYoung2026Recursive,
  author        = {Lemm, Marius and Nachtergaele, Bruno and Warzel, Simone and Young, Amanda},
  title         = {Recursive spectral relations and the charge vs neutral gap in fractional quantum {Hall} systems},
  journal       = {Journal of Mathematical Physics},
  volume        = {67},
  number        = {1},
  pages         = {011901},
  year          = {2026},
  month         = jan,
  doi           = {10.1063/5.0292975},
  url           = {https://doi.org/10.1063/5.0292975},
  eprint        = {2507.18814},
  archivePrefix = {arXiv},
  primaryClass  = {math-ph},
  note = {\href{https://doi.org/10.1063/5.0292975}{doi:10.1063/5.0292975}}
}

@misc{SchravenWarzel2026IMPS,
  author = {Schraven, Severin and Warzel, Simone},
  title = {Fractional Quantum {Hall} States: Infinite Matrix Product Representation and its Implications},
  year = {2026},
  eprint = {2601.12165},
  archivePrefix = {arXiv},
  primaryClass = {math-ph},
  note = {\href{https://arxiv.org/abs/2601.12165v1}{arXiv:2601.12165v1}, January 17, 2026},
  doi = {10.48550/arXiv.2601.12165},
  url = {https://arxiv.org/abs/2601.12165}
}

@article{OrtizNussinovDukelskySeidel,
  author = {Ortiz, G. and Nussinov, Z. and Dukelsky, J. and Seidel, A.},
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  eprint = {1306.3268},
  archivePrefix = {arXiv},
  note = {\href{https://doi.org/10.1103/PhysRevB.88.165303}{doi:10.1103/PhysRevB.88.165303}}
}

@article{Wick,
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@article{BartlettRudolphSpekkens,
  author = {Bartlett, Stephen D. and Rudolph, Terry and Spekkens, Robert W.},
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@article{PeyrlParrilo,
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@inproceedings{HouConference,
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@article{GaoLanzettaLedwithWangKhalaf,
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@article{GirvinJach,
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}