Bethe vectors ofGL(3)-invariant integrable models

2012/10/31 by S. Belliard, S. Pakuliak, E. Ragoucy +1 · 58 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Algebraic number #Algebraic structures and combinatorial models #Bethe ansatz #Integrable system #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Yangian #hep-th #math-ph #math.MP #msc:81R50 #msc:82B23

paper · pdf · doi:10.1088/1742-5468/2013/02/p02020

published in Journal of Statistical Mechanics Theory and Experiment 2013(02), P02020 (Institute of Physics) · 22 pages, typos corrected

arxiv created 2013/01/21 · openalex publication_date 2013/02/12 · arxiv updated 2015/06/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We study G L (3)-invariant integrable models solvable by the nested algebraic Bethe ansatz. Different formulas are given for the Bethe vectors and the actions of the generators of the Yangian 𝒴( g l 3 ) on the Bethe vectors are considered. These actions are relevant for the calculation of correlation functions and form factors of local operators of the underlying quantum models.

Citations

• Quantum Inverse Scattering Method and Correlation Functions
• A computation of an universal weight function for the quantum affine algebra U_q(\mathfrakgl_N)
• Jackson Integral Representations for Solutions to the Quantized Knizhnik-Zamolodchikov Equation
• The nested Bethe ansatz for ‘all’ closed spin chains
• Quantum inverse problem method. I
• Calculation of norms of Bethe wave functions
• Master equation for spin–spin correlation functions of the XXZ chain

Cited by

• GL(3) -Based Quantum Integrable Composite Models. II. Form Factors of Local Operators
• Form factors of local operators in a one-dimensional two-component Bose gas

Related

• GL(3)-Based Quantum Integrable Composite Models. I. Bethe Vectors
• Yangian Doubles and off-Shell Bethe Vectors
• GL(3) -Based Quantum Integrable Composite Models. II. Form Factors of Local Operators
• Resolution of the GL(3) - O(3) state labelling problem via O(3)-invariant Bethe subalgebra of the twisted Yangian
• Zero modes method and form factors in quantum integrable models