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

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

2006-04-17

arxiv.org/abs/math-ph/0604036v2

Nucl.Phys. B754 (2006) 309-328

Physics

Mathematical Physics

17 pages; LaTeX file with amssymb; v2: typos corrected, references added, to appear in Nucl.Phys.B

Scientific paper

10.1016/j.nuclphysb.2006.08.008

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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