Nested Algebraic Bethe Ansatz in integrable models: recent results

Abstract

This short note summarizes the works done in collaboration between S. Belliard (CEA, Saclay), L. Frappat (LAPTh, Annecy), S. Pakuliak (JINR, Dubna), E. Ragoucy (LAPTh, Annecy), N. Slavnov (Steklov Math. Inst., Moscow) and more recently A. Hutsalyuk (Wuppertal / Moscow) and A. Liashyk (Kiev / Moscow). It presents the construction of Bethe vectors, their scalar products and the form factors of local operator for integrable models based on the (super)algebras $g{l}_n$, $g{l}_{m|p}$ or their quantum deformations. It corresponds to two talks given by E.R. and N.S. at \textsl{Correlation functions of quantum integrable systems and beyond}, in honor of Jean-Michel Maillet for his 60's (ENS Lyon, October 2017).

arXiv comment22 pages, submitted to SciPost Phys

References in corpus (41)

• Form factors of the XXZ Heisenberg spin-1/2 finite chain
• On the quantum inverse scattering problem
• A New Supersymmetric and Exactly Solvable Model of Correlated Electrons
• Form factor approach to dynamical correlation functions in critical models
• Solution of the quantum inverse problem
• On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain
• Nested Bethe ansatz for "all" closed spin chains
• Form factor approach to the asymptotic behavior of correlation functions in critical models
• Thermodynamics and excitations of the one-dimensional Hubbard model
• Thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain
• New Construction of Eigenstates and Separation of Variables for SU(N) Quantum Spin Chains
• Bethe vectors of GL(3)-invariant integrable models
• Form factors in quantum integrable models with GL(3)-invariant R-matrix
• Highest coefficient of scalar products in SU(3)-invariant integrable models
• Long-distance asymptotic behaviour of multi-point correlation functions in massless quantum models
• Current presentation for the double super-Yangian $DY(\mathfrak{gl}(m|n))$ and Bethe vectors
• Form factors in SU(3)-invariant integrable models
• GL(3)-Based Quantum Integrable Composite Models. II. Form Factors of Local Operators
• Off-shell Bethe vectors and Drinfeld currents
• The algebraic Bethe ansatz for scalar products in SU(3)-invariant integrable models
• Scalar products of Bethe vectors in the models with $\mathfrak{gl}(m|n)$ symmetry
• GL(3)-Based Quantum Integrable Composite Models. I. Bethe Vectors
• Form factors of local operators in a one-dimensional two-component Bose gas
• Zero modes method and form factors in quantum integrable models
• Scalar products of Bethe vectors in models with $\mathfrak{gl}(2|1)$ symmetry 2. Determinant representation
• Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric $R$-Matrix
• Multiple Actions of the Monodromy Matrix in $\mathfrak{gl}(2|1)$-Invariant Integrable Models
• Multiple integral formulae for the scalar product of on-shell and off-shell Bethe vectors in SU(3)-invariant models
• Bethe Ansatz for the Universal Weight Function
• Bethe vectors for models based on the super-Yangian $Y(\mathfrak{gl}(m|n))$
• Bethe vectors of quantum integrable models based on Uq(gl(N))
• Bethe Ansatz and Bethe Vectors Scalar Products
• Norm of Bethe vectors in models with $\mathfrak{gl}(m|n)$ symmetry
• Scalar products in GL(3)-based models with trigonometric R-matrix. Determinant representation
• Form factors of the monodromy matrix entries in gl(2|1)-invariant integrable models
• Form factors of local operators in supersymmetric quantum integrable models
• Determinant representations for form factors in quantum integrable models with GL(3)-invariant R-matrix
• Semi-classical analysis of the inner product of Bethe states
• Scalar products in models with GL(3) trigonometric R-matrix. Highest coefficient
• Scalar products and norm of Bethe vectors for integrable models based on $U_q({\widehat{\mathfrak{gl}}}_n)$
• Scalar products in models with $GL(3)$ trigonometric $R$-matrix. General case

Cited by in corpus (6)

• Correlation functions and transport coefficients in generalised hydrodynamics
• Effective free-fermionic form factors and the XY spin chain
• On Scalar Products in Higher Rank Quantum Separation of Variables
• Complete spectrum of quantum integrable lattice models associated to ${\mathcal{U}}_q(\widehat{g{l}_n})$ by separation of variables
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint