The q-deformed analogue of the Onsager algebra: Beyond the Bethe ansatz approach |
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| Institution: | 1. Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany;2. Department of Theoretical Physics, Indian Association for the Cultivation of Science, 2A & 2B Raja S.C. Mullick Road, Kolkata 700032, India;1. Instytut Fizyki Teoretycznej, Uniwersytet Wrocławski, pl. M. Borna 9, 50-204 Wrocław, Poland;2. Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Joliot-Curie str. 6, 141980 Dubna, Russia;3. National Research Nuclear University (MEPhI), Kashirskoe Shosse 31, 115409 Moscow, Russia;4. Institut für Physik, Humboldt Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany;1. Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, I-00185 Rome, Italy;2. INFN, Sezione di Roma, Piazzale Aldo Moro 2, I-00185 Rome, Italy;3. PH Department, TH Unit, CERN, CH-1211 Geneva 23, Switzerland;4. Department of Physics, Theoretical Section, University of Trieste, Strada Costiera 11, I-34151 Trieste, Italy;5. INFN, Sezione di Trieste, Via Valerio 2, I-34127 Trieste, Italy;6. NICPB, Ravala 10, Tallinn 10143, Estonia |
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| Abstract: | The spectral properties of operators formed from generators of the q-Onsager non-Abelian infinite-dimensional algebra are investigated. Using a suitable functional representation, all eigenfunctions are shown to obey a second-order q-difference equation (or its degenerate discrete version). In the algebraic sector associated with polynomial eigenfunctions (or their discrete analogues), Bethe equations naturally appear. Beyond this sector, where the Bethe ansatz approach is not applicable in related massive quantum integrable models, the eigenfunctions are also described. The spin-half XXZ open spin chain with general integrable boundary conditions is reconsidered in light of this approach: all the eigenstates are constructed. In the algebraic sector which corresponds to special relations among the parameters, known results are recovered. |
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