Algebraic Bethe ansatz for the XXZ Heisenberg spin
chain with triangular boundaries and the corresponding
Gaudin model

Antonio, N. Cirilo; Manojlović,  Nenad; Salom, I.

http://hdl.handle.net/10400.1/11215

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Authors

Antonio, N. Cirilo

Manojlović, Nenad

Salom, I.

Abstract(s)

We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model. (C) 2014 The Authors. Published by Elsevier B.V.