Journal
NUCLEAR PHYSICS B
Volume 873, Issue 3, Pages 550-584Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.nuclphysb.2013.05.003
Keywords
XXZ open spin chain; q-Onsager algebra; q-vertex operators; Thermodynamic limit
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The half-infinite XXZ open spin chain with general integrable boundary conditions is considered within the recently developed 'Onsager's approach'. Inspired by the finite size case, for any type of integrable boundary conditions it is shown that the transfer matrix is simply expressed in terms of the elements of a new type of current algebra recently introduced. In the massive regime -1 < q < 0, level one infinite dimensional representation (q-vertex operators) of the new current algebra are constructed in order to diagonalize the transfer matrix. For diagonal boundary conditions, known results of Jimbo et al. are recovered. For upper (or lower) non-diagonal boundary conditions, a solution is proposed. Vacuum and excited states are formulated within the representation theory of the current algebra using q-bosons, opening the way for the calculation of integral representations of correlation functions for a non-diagonal boundary. Finally, for q generic the long standing question of the hidden non-Abelian symmetry of the Hamiltonian is solved: it is either associated with the q-Onsager algebra (generic non-diagonal case) or the augmented q-Onsager algebra (generic diagonal case). (C) 2013 Elsevier B.V. All rights reserved.
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