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On Form Factors in nested Bethe Ansatz systems  [PDF]
Balazs Pozsgay,Willem-Victor van Gerven Oei,Marton Kormos
Physics , 2012, DOI: 10.1088/1751-8113/45/46/465007
Abstract: We investigate form factors of local operators in the multi-component Quantum Non-linear Schr\"odinger model, a prototype theory solvable by the so-called nested Bethe Ansatz. We determine the analytic properties of the infinite volume form factors using the coordinate Bethe Ansatz solution and we establish a connection with the finite volume matrix elements. In the two-component models we derive a set of recursion relations for the "magnonic form factors", which are the matrix elements on the nested Bethe Ansatz states. In certain simple cases (involving states with only one spin-impurity) we obtain explicit solutions for the recursion relations.
SU(N) Matrix Difference Equations and a Nested Bethe Ansatz  [PDF]
H. Babujian,M. Karowski,A. Zapletal
Physics , 1996,
Abstract: A system of SU(N)-matrix difference equations is solved by means of a nested version of a generalized Bethe Ansatz, also called "off shell" Bethe Ansatz. The highest weight property of the solutions is proved. (Part I of a series of articles on the generalized nested Bethe Ansatz and difference equations.)
Algebraic nested Bethe ansatz for the elliptic Ruijsenaars model  [PDF]
E. Billey
Mathematics , 1998,
Abstract: The eigenvalues of the elliptic N-body Ruijsenaars operator are obtained by a dynamical version of the algebraic nested Bethe ansatz method. We use a result of Felder and Varchenko, who showed how to obtain the Ruijsenaars operator as the transfer matrix of a particular representation of the elliptic quantum group associated to gl(N).
U(N) Matrix Difference Equations and a Nested Bethe Ansatz  [PDF]
H. Babujian,M. Karowski,A. Zapletal
Physics , 1996, DOI: 10.1088/0305-4470/30/18/019
Abstract: A system of U(N)-matrix difference equations is solved by means of a nested version of a generalized Bethe Ansatz. The highest weight property of the solutions is proved and some examples of solutions are calculated explicitly. (Part II of a series of articles on the generalized nested Bethe Ansatz and difference equations.)
Nested Bethe ansatz for "all" closed spin chains  [PDF]
S. Belliard,E. Ragoucy
Physics , 2008, DOI: 10.1088/1751-8113/41/29/295202
Abstract: We present in an unified and detailed way the Nested Bethe Ansatz for closed spin chains based on Y(gl(n)), Y(gl(m|n)), U_q(gl(n)) or U_q(gl(m|n)) (super)algebras, with arbitrary representations (i.e. `spins') on each site of the chain. In particular, the case of indecomposable representations of superalgebras is studied. The construction extends and unifies the results already obtained for spin chains based on Y(gl(n)) or U_q(gl(n)) and for some particular super-spin chains. We give the Bethe equations and the form of the Bethe vectors. The case of gl(2|1), gl(2|2$ and gl(4|4) superalgebras (that are related to AdS/CFT correspondence) is also detailed.
The Complex of Solutions of the Nested Bethe Ansatz. The A_2 Spin Chain  [PDF]
G. P. Pronko,Yu. G. Stroganov
Physics , 1999, DOI: 10.1088/0305-4470/33/46/309
Abstract: The full set of polynomial solutions of the nested Bethe Ansatz is constructed for the case of A_2 rational spin chain. The structure and properties of these associated solutions are more various then in the case of usual XXX (A_1) spin chain but their role is similar.
Nested Bethe ansatz for `all' open spin chains with diagonal boundary conditions  [PDF]
S. Belliard,E. Ragoucy
Physics , 2009, DOI: 10.1088/1751-8113/42/20/205203
Abstract: We present in an unified and detailed way the nested Bethe ansatz for open spin chains based on Y(gl(\fn)), Y(gl(\fm|\fn)), U_{q}(gl(\fn)) or U_{q}(gl(\fm|\fn)) (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 anstaz 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 fundamental representation and for some particular super-spin chains. We give the eigenvalues, Bethe equations and the form of the Bethe vectors for the corresponding models. The Bethe vectors are expressed using a trace formula.
Nested Bethe ansatz for Y(gl(n)) open spin chains with diagonal boundary conditions  [PDF]
S. Belliard,E. Ragoucy
Physics , 2010, DOI: 10.1134/S1547477111030058
Abstract: In this proceeding we present the nested Bethe ansatz for open spin chains of XXX-type, with arbitrary representations (i.e. `spins') on each site of the chain and diagonal boundary matrices $(K^+(u),K^-(u))$. The nested Bethe anstaz applies for a general $K^-(u)$, but a particular form of the $K^+(u)$ matrix. We give the eigenvalues, Bethe equations and the form of the Bethe vectors for the corresponding models. The Bethe vectors are expressed using a trace formula.
Functional relations and nested Bethe ansatz for sl(3) chiral Potts model at q^2=-1  [PDF]
H. E. Boos,V. V. Mangazeev
Physics , 1999, DOI: 10.1088/0305-4470/32/16/012
Abstract: We obtain the functional relations for the eigenvalues of the transfer matrix of the sl(3) chiral Potts model for q^2=-1. For the homogeneous model in both directions a solution of these functional relations can be written in terms of roots of Bethe ansatz-like equations. In addition, a direct nested Bethe ansatz has also been developed for this case.
Nested off-diagonal Bethe ansatz and exact solutions of the su(n) spin chain with generic integrable boundaries  [PDF]
Junpeng Cao,Wen-Li Yang,Kangjie Shi,Yupeng Wang
Physics , 2013, DOI: 10.1007/JHEP04(2014)143
Abstract: The nested off-diagonal Bethe ansatz method is proposed to diagonalize multi-component integrable models with generic integrable boundaries. As an example, the exact solutions of the su(n)-invariant spin chain model with both periodic and non-diagonal boundaries are derived by constructing the nested T-Q relations based on the operator product identities among the fused transfer matrices and the asymptotic behavior of the transfer matrices.
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