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Nested algebraic Bethe ansatz for open spin chains with even twisted Yangian symmetry
- Source :
- Ann. Henri Poincare 20 (2019), 339-392
- Publication Year :
- 2017
-
Abstract
- We present a nested algebraic Bethe ansatz for a one dimensional open spin chain whose boundary quantum spaces are irreducible $\mathfrak{so}_{2n}$- or $\mathfrak{sp}_{2n}$-representations and the monodromy matrix satisfies the defining relations of the Olshanskii twisted Yangian $Y^\pm(\mathfrak{gl}_{2n})$. We use a generalization of the Bethe ansatz introduced by De Vega and Karowski which allows us to relate the spectral problem of a $\mathfrak{so}_{2n}$- or $\mathfrak{sp}_{2n}$-symmetric open spin chain to that of a $\mathfrak{gl}_{n}$-symmetric periodic spin chain. We explicitly derive the structure of the Bethe vectors and the nested Bethe equations.<br />Comment: 36 pages; v.2: minor corrections, a trace formula for the Bethe vectors added
Details
- Database :
- arXiv
- Journal :
- Ann. Henri Poincare 20 (2019), 339-392
- Publication Type :
- Report
- Accession number :
- edsarx.1710.08409
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s00023-018-0731-1