arXiv:1909.12123 · Nuclear Physics B

Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains

Allan John Gerrard, Vidas Regelskis

Published Jan 2, 2020• 7 citations

Abstract

We present a nested algebraic Bethe ansatz for one-dimensional so2n- and sp2n-symmetric open spin chains with diagonal boundary conditions. The monodromy matrix of these spin chains satisfies the defining relations on the extended twisted Yangians Xρ(so2n,so2nρ)tw and Xρ(sp2n,sp2nρ)tw, respectively. We use a generalisation of the De Vega and Karowski approach allowing us to relate the spectral problem of so2n- or sp2n-symmetric open spin chain to that of gln-symmetric open spin chain studied by Belliard and Ragoucy. We explicitly derive the structure of Bethe vectors, their eigenvalues and the nested Bethe equations. We also provide a proof of Belliard and Ragoucy's trace formula for Bethe vectors of gln-symmetric open spin chains.

DOI: 10.1016/j.nuclphysb.2019.114909

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