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The q-deformed analogue of the Onsager algebra: beyond the Bethe ansatz approach

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 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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https://hal.archives-ouvertes.fr/hal-00082312
Contributor : Pascal Baseilhac Connect in order to contact the contributor
Submitted on : Tuesday, June 27, 2006 - 2:04:59 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:08 PM

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Pascal Baseilhac. The q-deformed analogue of the Onsager algebra: beyond the Bethe ansatz approach. 2006. ⟨hal-00082312⟩

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