Nested algebraic Bethe ansatz for deformed orthogonal and symplectic spin chains

Abstract

We construct exact eigenvectors and eigenvalues for $U_q({\mathfrak{sp}}_{2n})$- and $U_q({\mathfrak{so}}_{2n})$-symmetric closed spin chains by means of a nested algebraic Bethe ansatz method. We use a fusion procedure to construct higher-dimensional Lax operators. Our approach generalises and extends the results obtained by Reshetikhin and De Vega-Karowski. We also present a generalisation of Tarasov-Varchenko trace formula for nested Bethe vectors.

arXiv comment22 pages, v2: final version

References in corpus (10)

• The algebraic Bethe ansatz for rational braid-monoid lattice models
• Nested Bethe ansatz for "all" closed spin chains
• Analytic Bethe Ansatz for Fundamental Representations of Yangians
• Jackson Integral Representations for Solutions to the Quantized Knizhnik-Zamolodchikov Equation
• Combinatorial Formulae for Nested Bethe Vectors
• A new fusion procedure for the Brauer algebra and evaluation homomorphisms
• Nonstandard Bethe Ansatz equations for open O(N) spin chains
• Bethe Ansatz and exact form factors of the O(N) Gross Neveu-model
• Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains
• The Nested Off-shell Bethe ansatz and O(N) Matrix Difference Equations

Cited by in corpus (5)

• Correlation functions and transport coefficients in generalised hydrodynamics
• QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains
• Algebraic Bethe ansatz for ${\mathfrak{o}}_{2n+1}$-invariant integrable models
• Higher rank elliptic partition functions and multisymmetric elliptic functions
• Multiple commutation relations of the quantum affine algebra $U_q({\widehat{\mathfrak{gl}}}_N)$, nested Bethe vector and the Gelfand-Tsetlin basis