14 research outputs found
Off-shell Bethe vectors and Drinfeld currents
In this paper we compare two constructions of weight functions (off-shell
Bethe vectors) for the quantum affine algebra . The
first construction comes from the algebraic nested Bethe ansatz. The second one
is defined in terms of certain projections of products of Drinfeld currents. We
show that two constructions give the same result in tensor products of vector
representations of .Comment: 25 pages, misprints correcte
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" 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
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
Thermodynamical limit of general gl(N) spin chains II: Excited states and energies
We consider the thermodynamical limit of a gl(N) spin chain with arbitrary
representation at each site of the chain. We consider excitations (with holes
and new strings) above the vacuum and compute their corrections in 1/L to the
densities and the energy.Comment: 29 pages misprints in the example of sect 5.1 amended and a mistake
in theorem 5.4 correcte