Nested Algebraic Bethe Ansatz for Open Spin Chains with Even Twisted Yangian Symmetry

Allan John Gerrard, Niall James MacKay, Vidas Regelskis

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We present a nested algebraic Bethe ansatz for a one dimensional open spin chain whose boundary quantum spaces are irreducible so2n- or sp2n-representations and the monodromy matrix satisfies the defining relations of the Olshanskii twisted Yangian Y±(gl2n). We use a generalization of the Bethe ansatz introduced by De Vega and Karowski which allows us to relate the spectral problem of a so2n- or sp2n-symmetric open spin chain to that of a gln-symmetric periodic spin chain. We explicitly derive the structure of the Bethe vectors and the nested Bethe equations.
Original languageEnglish
Pages (from-to)339-392
Number of pages54
JournalAnnales Henri Poincare
Issue number2
Early online date24 Oct 2018
Publication statusPublished - 5 Feb 2019

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