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Theoretical and Mathematical Physics

Nested Bethe Ansatz for the RTT Algebra of sp(4) Type

Č. Burdík, Ondřej Navrátil

Published Jan 1, 2019• 9 citations
Publisher

Abstract

We show how to formulate the algebraic nested Bethe ansatz for RTT algebras with an R-matrix of the sp( 4 ) type. We obtain the Bethe vectors and Bethe conditions for any highest-weight representation of these RTT algebras.
DOI
10.1134/s004057791901001x

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Abstract We study the highest weight representations of the RTT-algebras for the R-matrix of spq(4)\mathop {{\text{sp}}}\nolimits_q (4)spq​(4) type by the nested algebraic Bethe ansatz. It is a generalization of our study for R-matrix of sp(4){\text{sp}}(4)sp(4) .
We study the highest weight representations of the RTT-algebras for the R-matrix of sp(2n)sp(2n)sp(2n) type by the nested algebraic Bethe ansatz. For special representations these models were solved by Reshetikhin and by Martins and Ramos.
We present in a unified and detailed way the nested Bethe ansatz for open spin chains based on(super)algebras, with arbitrary representations (i.e., 'spins') on each site of the chain and diagonal boundary matrices (K + (u), K -(u)).The nested Bethe ansatz applies for a general K -(u), but a particular form of the K + (u) matrix.The construction extends and unifies the results already obtained for open spin chains based on the fundamental representation and for some particular superspin chains.We give the eigenvalues, Bethe equations and the explicit form of the Bethe vectors for the corresponding models.The Bethe vectors are also expressed using a trace formula.