{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:31:25Z","timestamp":1746804685115,"version":"3.40.5"},"reference-count":55,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2022,6,14]],"date-time":"2022-06-14T00:00:00Z","timestamp":1655164800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NSF","award":["DMR-2011750"],"award-info":[{"award-number":["DMR-2011750"]}]},{"DOI":"10.13039\/100000936","name":"the Gordon and Betty Moore Foundation","doi-asserted-by":"crossref","award":["GBMF8685"],"award-info":[{"award-number":["GBMF8685"]}],"id":[{"id":"10.13039\/100000936","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000879","name":"Alfred P. Sloan Foundation","doi-asserted-by":"crossref","award":["2021 Sloan Research Fellowship"],"award-info":[{"award-number":["2021 Sloan Research Fellowship"]}],"id":[{"id":"10.13039\/100000879","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>We investigate the homogeneous chiral edge theory of the filling <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>&amp;#x03BD;<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>4<\/mml:mn><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>\/<\/mml:mo><\/mml:mrow><mml:mn>3<\/mml:mn><\/mml:math> fractional quantum Hall state, which is parameterized by a Luttinger liquid velocity matrix and an electron tunneling amplitude (ignoring irrelevant terms). We identify two solvable cases: one case where the theory gives two free chiral boson modes, and the other case where the theory yields one free charge <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mfrac><mml:mrow><mml:mn>2<\/mml:mn><mml:mi>e<\/mml:mi><\/mml:mrow><mml:msqrt><mml:mn>3<\/mml:mn><\/mml:msqrt><\/mml:mfrac><\/mml:math> chiral fermion and two free chiral Bogoliubov (Majorana) fermions. For generic parameters, the energy spectrum from our exact diagonalization shows Poisson level spacing statistics (LSS) in each conserved charge and momentum sector, indicating the existence of hidden conserved quantities and the possibility that the generic edge theory of the <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>&amp;#x03BD;<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>4<\/mml:mn><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>\/<\/mml:mo><\/mml:mrow><mml:mn>3<\/mml:mn><\/mml:math> fractional quantum Hall state is integrable. We further show that a global symmetry preserving irrelevant nonlinear kinetic term will lead to the transition of LSS from Poisson to Wigner-Dyson at high energies. This further supports the possibility that the model without irrelevant terms is integrable.<\/jats:p>","DOI":"10.22331\/q-2022-06-14-736","type":"journal-article","created":{"date-parts":[[2022,6,14]],"date-time":"2022-06-14T11:24:14Z","timestamp":1655205854000},"page":"736","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Integrability of the <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>&amp;#x3BD;<\/mml:mo><\/mml:mrow><mml:mo>=<\/mml:mo><mml:mn>4<\/mml:mn><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>\/<\/mml:mo><\/mml:mrow><mml:mn>3<\/mml:mn><\/mml:math> fractional quantum Hall edge states"],"prefix":"10.22331","volume":"6","author":[{"given":"Yichen","family":"Hu","sequence":"first","affiliation":[{"name":"Department of Physics, Princeton University, Princeton, New Jersey 08544, USA"},{"name":"The Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Biao","family":"Lian","sequence":"additional","affiliation":[{"name":"Department of Physics, Princeton University, Princeton, New Jersey 08544, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2022,6,14]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"I. 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