{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,26]],"date-time":"2026-04-26T07:44:20Z","timestamp":1777189460526,"version":"3.51.4"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,5,6]],"date-time":"2023-05-06T00:00:00Z","timestamp":1683331200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,5,6]],"date-time":"2023-05-06T00:00:00Z","timestamp":1683331200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["PTDC\/MAT-PUR\/30234\/2017"],"award-info":[{"award-number":["PTDC\/MAT-PUR\/30234\/2017"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["IF\/00069\/2015"],"award-info":[{"award-number":["IF\/00069\/2015"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/00208\/2020"],"award-info":[{"award-number":["UIDB\/00208\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Commun. Math. Phys."],"published-print":{"date-parts":[[2023,8]]},"DOI":"10.1007\/s00220-023-04728-3","type":"journal-article","created":{"date-parts":[[2023,5,6]],"date-time":"2023-05-06T16:01:21Z","timestamp":1683388881000},"page":"335-390","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["On Solutions of the Bethe Ansatz for the Quantum KdV Model"],"prefix":"10.1007","volume":"402","author":[{"given":"Riccardo","family":"Conti","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7547-4804","authenticated-orcid":false,"given":"Davide","family":"Masoero","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,5,6]]},"reference":[{"issue":"2","key":"4728_CR1","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1007\/s00220-004-1112-9","volume":"249","author":"A Avila","year":"2004","unstructured":"Avila, A.: Convergence of an exact quantization scheme. Commun. Math. Phys. 249(2), 305\u2013318 (2004)","journal-title":"Commun. Math. Phys."},{"key":"4728_CR2","unstructured":"Baxter, R.: Exactly Solved Models in Statistical Mechanics. Elsevier (2016)"},{"key":"4728_CR3","doi-asserted-by":"publisher","DOI":"10.1016\/j.nuclphysb.2021.115337","volume":"965","author":"V Bazhanov","year":"2021","unstructured":"Bazhanov, V., Kotousov, G., Koval, S., Lukyanov, S.: Scaling limit of the z2 invariant inhomogeneous six-vertex model. Nucl. Phys. B 965, 115337 (2021)","journal-title":"Nucl. Phys. B"},{"issue":"2","key":"4728_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF02101898","volume":"177","author":"V Bazhanov","year":"1996","unstructured":"Bazhanov, V., Lukyanov, S., Zamolodchikov, A.: Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz. Commun. Math. Phys. 177(2), 1 (1996)","journal-title":"Commun. Math. Phys."},{"issue":"2","key":"4728_CR5","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/s002200050240","volume":"190","author":"V Bazhanov","year":"1997","unstructured":"Bazhanov, V., Lukyanov, S., Zamolodchikov, A.: Integrable structure of conformal field theory II. Q-operator and DDV equation. Commun. Math. Phys. 190(2), 247\u2013278 (1997)","journal-title":"Commun. Math. Phys."},{"key":"4728_CR6","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1023\/A:1004838616921","volume":"102","author":"V Bazhanov","year":"2001","unstructured":"Bazhanov, V., Lukyanov, S., Zamolodchikov, A.: Spectral determinants for Schrodinger equation and Q operators of conformal field theory. J. Statist. Phys. 102, 567\u2013576 (2001)","journal-title":"J. Statist. Phys."},{"key":"4728_CR7","doi-asserted-by":"publisher","first-page":"711","DOI":"10.4310\/ATMP.2003.v7.n4.a4","volume":"7","author":"V Bazhanov","year":"2004","unstructured":"Bazhanov, V., Lukyanov, S., Zamolodchikov, A.: Higher-level eigenvalues of Q-operators and Schroedinger equation. Adv. Theor. Math. Phys. 7, 711 (2004)","journal-title":"Adv. Theor. Math. Phys."},{"issue":"3","key":"4728_CR8","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1007\/BF01341708","volume":"71","author":"H Bethe","year":"1931","unstructured":"Bethe, H.: Zur theorie der metalle. Z. Phys. 71(3), 205\u2013226 (1931)","journal-title":"Z. Phys."},{"key":"4728_CR9","doi-asserted-by":"publisher","first-page":"059","DOI":"10.1007\/JHEP02(2021)059","volume":"02","author":"R Conti","year":"2021","unstructured":"Conti, R., Masoero, D.: Counting monster potentials. JHEP 02, 059 (2021)","journal-title":"JHEP"},{"key":"4728_CR10","doi-asserted-by":"publisher","first-page":"2313","DOI":"10.1103\/PhysRevLett.69.2313","volume":"69","author":"C Destri","year":"1992","unstructured":"Destri, C., de Vega, H.J.: New thermodynamic Bethe ansatz equations without strings. Phys. Rev. Lett. 69, 2313\u20132317 (1992)","journal-title":"Phys. Rev. Lett."},{"issue":"22","key":"4728_CR11","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ab83c9","volume":"53","author":"P Dorey","year":"2020","unstructured":"Dorey, P., Dunning, C., Negro, S., Tateo, R.: Geometric aspects of the ode\/im correspondence. J. Phys. A: Math. Theor. 53(22), 223001 (2020)","journal-title":"J. Phys. A: Math. Theor."},{"issue":"32","key":"4728_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1088\/1751-8113\/40\/32\/R01","volume":"40","author":"P Dorey","year":"2007","unstructured":"Dorey, P., Dunning, C., Tateo, R.: The ODE\/IM correspondence. J. Phys. A Math. Theor. 40(32), 1 (2007)","journal-title":"J. Phys. A Math. Theor."},{"issue":"3","key":"4728_CR13","doi-asserted-by":"publisher","first-page":"573","DOI":"10.1016\/S0550-3213(99)00609-4","volume":"563","author":"P Dorey","year":"1999","unstructured":"Dorey, P., Tateo, R.: On the relation between Stokes multipliers and the T-Q systems of conformal field theory. Nucl. Phys. B 563(3), 573\u2013602 (1999)","journal-title":"Nucl. Phys. B"},{"key":"4728_CR14","unstructured":"Dunning, C.: PhD thesis, Durham University (2000)"},{"key":"4728_CR15","unstructured":"Erd\u00e9lyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.: Higher Transcendental Functions, vol. 1. McGraw-Hill Book Company Inc, New York (1953)"},{"key":"4728_CR16","doi-asserted-by":"crossref","unstructured":"Eremenko, A.: Entire functions, PT-symmetry and Voros\u2019s quantization scheme. Matematychni Studii 54(2), 203\u2013210 (2020)","DOI":"10.30970\/ms.54.2.203-210"},{"key":"4728_CR17","doi-asserted-by":"crossref","unstructured":"Faddeev, L.: Instructive history of the quantum inverse scattering method. In: KdV 95, pp. 69\u201384. Springer (1995)","DOI":"10.1007\/978-94-011-0017-5_3"},{"key":"4728_CR18","doi-asserted-by":"crossref","unstructured":"Feigin, B., Frenkel, E.: Quantization of soliton systems and Langlands duality. In: Exploring New Structures and Natural Constructions in Mathematical Physics, volume 61 of Adv. Stud. Pure Math., pp. 185\u2013274. Math. Soc. Japan, Tokyo (2011)","DOI":"10.2969\/aspm\/06110185"},{"issue":"23\u201324","key":"4728_CR19","doi-asserted-by":"publisher","first-page":"2131","DOI":"10.1016\/j.physd.2012.08.008","volume":"241","author":"G Felder","year":"2012","unstructured":"Felder, G., Hemery, A., Veselov, A.: Zeros of Wronskians of Hermite polynomials and young diagrams. Physica D 241(23\u201324), 2131\u20132137 (2012)","journal-title":"Physica D"},{"issue":"1\u20132","key":"4728_CR20","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1016\/j.physletb.2005.01.037","volume":"609","author":"D Fioravanti","year":"2005","unstructured":"Fioravanti, D.: Geometrical loci and CFTs via the Virasoro symmetry of the mKdV-SG hierarchy: an excursus. Phys. Lett. B 609(1\u20132), 173\u2013179 (2005)","journal-title":"Phys. Lett. B"},{"issue":"1\u20134","key":"4728_CR21","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/S0370-2693(96)01409-8","volume":"390","author":"D Fioravanti","year":"1997","unstructured":"Fioravanti, D., Mariottini, A., Quattrini, E., Ravanini, F.: Excited state Destri-De vega equation for sine-gordon and restricted sine-Gordon models. Phys. Lett. B 390(1\u20134), 243\u2013251 (1997)","journal-title":"Phys. Lett. B"},{"issue":"07","key":"4728_CR22","doi-asserted-by":"publisher","first-page":"031","DOI":"10.1088\/1126-6708\/2003\/07\/031","volume":"2003","author":"D Fioravanti","year":"2003","unstructured":"Fioravanti, D., Rossi, M.: Exact conserved quantities on the cylinder I: conformal case. J. High Energy Phys. 2003(07), 031 (2003)","journal-title":"J. High Energy Phys."},{"issue":"2","key":"4728_CR23","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1007\/s00220-018-3194-9","volume":"362","author":"E Frenkel","year":"2018","unstructured":"Frenkel, E., Hernandez, D.: Spectra of quantum Kdv hamiltonians, Langlands duality, and affine opers. Commun. Math. Phys. 362(2), 361\u2013414 (2018)","journal-title":"Commun. Math. Phys."},{"key":"4728_CR24","doi-asserted-by":"crossref","unstructured":"Gaudin, M.: The Bethe Wavefunction. Cambridge University Press (2014)","DOI":"10.1017\/CBO9781107053885"},{"issue":"3","key":"4728_CR25","doi-asserted-by":"publisher","first-page":"941","DOI":"10.1007\/s00023-019-00866-4","volume":"21","author":"L Hilfiker","year":"2020","unstructured":"Hilfiker, L., Runkel, I.: Existence and uniqueness of solutions to y-systems and tba equations. Ann. Henri Poincar\u00e9 21(3), 941\u2013991 (2020)","journal-title":"Ann. Henri Poincar\u00e9"},{"key":"4728_CR26","first-page":"11","volume":"26","author":"L Hulth\u00e9n","year":"1938","unstructured":"Hulth\u00e9n, L.: \u00dcber das Austauschproblem eines Kristalles. Ark. Fys. A 26, 11 (1938)","journal-title":"Ark. Fys. A"},{"issue":"13","key":"4728_CR27","doi-asserted-by":"publisher","first-page":"3111","DOI":"10.1088\/0305-4470\/24\/13\/025","volume":"24","author":"A Klumper","year":"1991","unstructured":"Klumper, A., Batchelor, M., Pearce, P.: Central charges of the 6-and 19-vertex models with twisted boundary conditions. J. Phys. A: Math. Gen. 24(13), 3111 (1991)","journal-title":"J. Phys. A: Math. Gen."},{"issue":"3","key":"4728_CR28","doi-asserted-by":"publisher","first-page":"1009","DOI":"10.1007\/s00220-017-3066-8","volume":"357","author":"K Kozlowski","year":"2018","unstructured":"Kozlowski, K.: On condensation properties of Bethe roots associated with the xxz chain. Commun. Math. Phys. 357(3), 1009\u20131069 (2018)","journal-title":"Commun. Math. Phys."},{"key":"4728_CR29","doi-asserted-by":"crossref","unstructured":"Levin, B.: Lectures on Entire Functions, volume 150. American Mathematical Soc. (1996)","DOI":"10.1090\/mmono\/150"},{"issue":"1","key":"4728_CR30","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1103\/PhysRev.162.162","volume":"162","author":"E Lieb","year":"1967","unstructured":"Lieb, E.: Residual entropy of square ice. Phys. Rev. 162(1), 162 (1967)","journal-title":"Phys. Rev."},{"key":"4728_CR31","doi-asserted-by":"publisher","first-page":"008","DOI":"10.1007\/JHEP07(2010)008","volume":"1007","author":"SL Lukyanov","year":"2010","unstructured":"Lukyanov, S.L., Zamolodchikov, A.B.: Quantum Sine(h)-Gordon model and classical integrable equations. JHEP 1007, 008 (2010)","journal-title":"JHEP"},{"issue":"1","key":"4728_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00220-020-03792-3","volume":"378","author":"D Masoero","year":"2020","unstructured":"Masoero, D., Raimondo, A.: Opers for higher states of quantum kdv models. Commun. Math. Phys. 378(1), 1\u201374 (2020)","journal-title":"Commun. Math. Phys."},{"issue":"3","key":"4728_CR33","doi-asserted-by":"publisher","first-page":"719","DOI":"10.1007\/s00220-016-2643-6","volume":"344","author":"D Masoero","year":"2016","unstructured":"Masoero, D., Raimondo, A., Valeri, D.: Bethe Ansatz and the spectral theory of affine lie algebra-valued connections I. The simply-laced Case. Commun. Math. Phys. 344(3), 719\u2013750 (2016)","journal-title":"Commun. Math. Phys."},{"issue":"3","key":"4728_CR34","doi-asserted-by":"publisher","first-page":"1063","DOI":"10.1007\/s00220-016-2744-2","volume":"349","author":"D Masoero","year":"2017","unstructured":"Masoero, D., Raimondo, A., Valeri, D.: Bethe Ansatz and the Spectral Theory of Affine Lie algebra-Valued Connections II: The Non Simply-Laced Case. Commun. Math. Phys. 349(3), 1063\u20131105 (2017)","journal-title":"Commun. Math. Phys."},{"issue":"4","key":"4728_CR35","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1007\/BF01961236","volume":"82","author":"H McKean","year":"1982","unstructured":"McKean, H., Trubowitz, E.: The spectral class of the quantum-mechanical harmonic oscillator. Commun. Math. Phys. 82(4), 471\u2013495 (1982)","journal-title":"Commun. Math. Phys."},{"key":"4728_CR36","unstructured":"Negro, S.: Excited states DDV. Private communication"},{"issue":"3","key":"4728_CR37","doi-asserted-by":"publisher","first-page":"1574","DOI":"10.1007\/BF02557204","volume":"121","author":"A Oblomkov","year":"1999","unstructured":"Oblomkov, A.: Monodromy-free schr\u00f6dinger operators with quadratically increasing potentials. Theor. Math. Phys. 121(3), 1574\u20131584 (1999)","journal-title":"Theor. Math. Phys."},{"issue":"2","key":"4728_CR38","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1103\/PhysRev.112.309","volume":"112","author":"R Orbach","year":"1958","unstructured":"Orbach, R.: Linear antiferromagnetic chain with anisotropic coupling. Phys. Rev. 112(2), 309 (1958)","journal-title":"Phys. Rev."},{"issue":"5","key":"4728_CR39","first-page":"13","volume":"34","author":"L Takhtadzhyan","year":"1979","unstructured":"Takhtadzhyan, L., Faddeev, L.: The quantum method of the inverse problem and the heisenberg xyz model. Uspekhi Matematicheskikh Nauk 34(5), 13\u201363 (1979)","journal-title":"Uspekhi Matematicheskikh Nauk"},{"key":"4728_CR40","doi-asserted-by":"crossref","unstructured":"Voros, A.: Exact anharmonic quantization condition (in one dimension). In: Quasiclassical Methods, pp. 189\u2013224 (1997)","DOI":"10.1007\/978-1-4612-1940-8_10"},{"key":"4728_CR41","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1103\/PhysRev.150.321","volume":"150","author":"CN Yang","year":"1966","unstructured":"Yang, C.N., Yang, C.P.: One-dimensional chain of anisotropic spin-spin interactions. i. proof of Bethe\u2019s hypothesis for ground state in a finite system. Phys. Rev. 150, 321\u2013327 (1966)","journal-title":"Phys. Rev."},{"issue":"31","key":"4728_CR42","doi-asserted-by":"publisher","first-page":"6747","DOI":"10.1088\/0305-4470\/31\/31\/019","volume":"31","author":"P Zinn-Justin","year":"1998","unstructured":"Zinn-Justin, P.: Nonlinear integral equations for complex affine Toda models associated with simply laced lie algebras. J. Phys. A: Math. Gen. 31(31), 6747 (1998)","journal-title":"J. Phys. A: Math. Gen."}],"container-title":["Communications in Mathematical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00220-023-04728-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00220-023-04728-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00220-023-04728-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,19]],"date-time":"2024-10-19T22:51:57Z","timestamp":1729378317000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00220-023-04728-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,6]]},"references-count":42,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["4728"],"URL":"https:\/\/doi.org\/10.1007\/s00220-023-04728-3","relation":{},"ISSN":["0010-3616","1432-0916"],"issn-type":[{"value":"0010-3616","type":"print"},{"value":"1432-0916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,6]]},"assertion":[{"value":"7 February 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 April 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 May 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}