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For it to be a faithful characterization of quantum integrability, it should distinguish quantum systems with a well-defined classical limit in the same way as the unequivocal classical integrability criteria. We examine the proposed diagnostic in the class of collective spin models characterized by permutation symmetry in the spins. The well-known Lipkin-Meshov-Glick (LMG) model is a paradigmatic integrable system in this class with a well-defined classical limit. Thus, this model is an excellent testbed for examining quantum integrability diagnostics. First, we calculate analytically the average EE of the Dicke basis{<\/mml:mo>|<\/mml:mo><\/mml:mrow>j<\/mml:mi>,<\/mml:mo>m<\/mml:mi>&#x27E9;<\/mml:mo>}<\/mml:mo>m<\/mml:mi>=<\/mml:mo>&#x2212;<\/mml:mo>j<\/mml:mi><\/mml:mrow>j<\/mml:mi><\/mml:msubsup><\/mml:math>in any non-vanishing bipartition, and show that in the thermodynamic limit, it converges to1<\/mml:mn>\/<\/mml:mo><\/mml:mrow>2<\/mml:mn><\/mml:math>of the maximal EE in the corresponding bipartition. Using finite-size scaling, we numerically demonstrate that the aforementioned average EE in the thermodynamic limit is universal for all parameter values of the LMG model. Our analysis illustrates how a value of the average EE far away from the maximal in the thermodynamic limit could be a signature of integrability.<\/jats:p>","DOI":"10.22331\/q-2022-04-27-701","type":"journal-article","created":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T15:55:22Z","timestamp":1651074922000},"page":"701","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":12,"title":["Eigenstate entanglement in integrable collective spin models"],"prefix":"10.22331","volume":"6","author":[{"given":"Meenu","family":"Kumari","sequence":"first","affiliation":[{"name":"Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u00c1lvaro M.","family":"Alhambra","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut fur Quantenoptik, D-85748 Garching, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2022,4,27]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Vladimir Igorevich Arnol'd. ``Mathematical methods of classical mechanics''. 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