Algebraic Bethe ansatz for open XXX model with triangular boundary matrices

We consider open XXX spins chain with two general boundary matrices submitted to one constraint, which is equivalent to the possibility to put the two matrices in a triangular form. We construct Bethe vectors from a generalized algebraic Bethe ansatz. As usual, the method also provides Bethe equations and transfer matrix eigenvalues.Comment: 10 pge

Form factors in SU(3)-invariant integrable models

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. We obtain determinant representations for form factors of diagonal entries of the monodromy matrix. This representation can be used for the calculation of form factors and correlation functions of the XXX SU(3)-invariant Heisenberg chain.Comment: 15 pages; typos correcte

Bethe vectors of GL(3)-invariant integrable models

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. Different formulas are given for the Bethe vectors and the actions of the generators of the Yangian Y(sl(3)) on 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.Comment: 22 pages, typos correcte

Universal Bethe Ansatz and Scalar Products of Bethe Vectors

An integral presentation for the scalar products of nested Bethe vectors for the quantum integrable models associated with the quantum affine algebra Uq(gl₃) is given. This result is obtained in the framework of the universal Bethe ansatz, using presentation of the universal Bethe vectors in terms of the total currents of a ''new'' realization of the quantum affine algebra Uq(gl₃)

Highest coefficient of scalar products in SU(3)-invariant integrable models

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of a bilinear combination of their highest coefficients. We obtain various different representations for the highest coefficient in terms of sums over partitions. We also obtain multiple integral representations for the highest coefficient.Comment: 17 page

Nested Bethe ansatz for `all' open spin chains with diagonal boundary conditions

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.Comment: 40 pages; examples of Bethe vectors added; Bethe equations for U_q(gl(2/2)) added; misprints correcte

Nested Bethe ansatz for Y(gl(n)) open spin chains with diagonal boundary conditions

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.Comment: 15 pages, proceeding for Dubna International SQS 09 Worksho

Nested Bethe ansatz for "all" closed spin chains

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.Comment: 30 pages; New section on indecomposable representations added and the case of gl(2|1), gl(2|2) and gl(4|4) superalgebras (that are related to AdS/CFT correspondence) is also detaile

New reflection matrices for the U_q(gl(m|n)) case

We examine super symmetric representations of the B-type Hecke algebra. We exploit such representations to obtain new non-diagonal solutions of the reflection equation associated to the super algebra U_q(gl(m|n)). The boundary super algebra is briefly discussed and it is shown to be central to the super symmetric realization of the B-type Hecke algebraComment: 13 pages, Latex. A few alterations regarding the representations. A reference adde