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Physics of Atomic Nuclei

On Nested Bethe Ansatz for RTT Algebra of o(2n) Type

Č. Burdík, Ondřej Navrátil

Published Nov 1, 2018• 4 citations
Publisher

Abstract

We study the highest weight representations of the RTT algebras for the R matrix of o (2 n ) type by the nested algebraic Bethe ansatz. We show how auxiliary RTT algebra à can be used to find Bethe vectors and Bethe conditions. For special representations, in which representation of RTT algebra à is trivial, the problem was solved by Reshetikhin.

DOI
10.1134/s106377881806008x

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Scalar products of Bethe vectors in models with gl(2∣1)\mathfrak{gl}(2|1)gl(2∣1) symmetry 1. Super-analog of Reshetikhin formula
We study scalar products of Bethe vectors in integrable models solvable by nested algebraic Bethe ansatz and possessing gl(2∣1)\mathfrak{gl}(2|1)gl(2∣1) symmetry. Using explicit formulas of the monodromy matrix entries multiple actions onto Bethe vectors we obtain a representation for the scalar product in the most general case. This explicit representation appears to be a sum over partitions of the Bethe parameters. It can be used for the analysis of scalar products involving on-shell Bethe vectors. As a by-product, we obtain a determinant representation for the scalar products of generic Bethe vectors in integrable models with gl(1∣1)\mathfrak{gl}(1|1)gl(1∣1) symmetry.