Non-diagonal solutions to reflection equations in su(n) spin chains

Based on the recent formulation of a general scheme to construct boundary Lax pairs, we develop this systematic construction for the A (1) n affine Toda field theories (ATFT). We work out explicitly the first two models of the hierarchy, i.e. the sineGordon (A Toda theory is the first non-trivial example of the hierarchy that exhibits two distinct types of boundary conditions. We provide here novel expressions of boundary Lax pairs associated to both types of boundary conditions.

Section: Commentsmentioning

confidence: 99%

Boundary Lax pairs for the Toda field theories

Avan

Doikou

2009

“…Here we also note that the solutions D 1 and D 4 are the diagonal solutions derived by the first time in [21] and K I 13 is the non-diagonal solution derived in [20].…”

Section: B the Amentioning

confidence: 99%

An−1(1) reflection K-matrices

Lima-Santos

2002

We investigate the possible regular solutions of the boundary Yang-Baxter equation for the vertex models associated with the A (1) n−1 affine Lie algebra. We have classified them in two classes of solutions. The first class consists of n(n − 1)/2 K-matrix solutions with three free parameters. The second class are solutions that depend on the parity of n. For n odd there exist n reflection Kmatrices with 2 + [n/2] free parameters. It turns out that for n even there exist n/2 K-matrices with 2 + n/2 free parameters and n/2 K-matrices with 1 + n/2 free parameters.

“…The relations (31) together with the Eq. (29) imply that |Ψ 0 is an eigenvector of T (l,m) (λ) whose respective eigenvalue is…”

Section: Algebraic Bethe Ansatzmentioning

confidence: 99%

“…Non-diagonal solutions of the reflection equations are known for a variety of integrable models based on q-deformed Lie algebras [29,30,31] but similar results concerning superalgebras, where the supersymmetric t-J model is inserted, are still concentrated on the U q [osp(1|2)] symmetry [32] and on diagonal solutions [33]. The main result of this paper is to show that the covering transfer matrix of the supersymmetric t-J model built from a general non-diagonal so-lution of the reflection equation possess a trivial reference state needed to initiate an algebraic Bethe ansatz analysis.…”

Section: Introductionmentioning

confidence: 99%

Spectrum of the supersymmetric model with non-diagonal open boundaries

Galleas

2007

In this work we diagonalize the double-row transfer matrix of the supersymmetric t-J model with non-diagonal boundary terms by means of the algebraic Bethe ansatz. The corresponding reflection equations are studied and two distinct classes of solutions are found, one diagonal solution and other non-diagonal. In the non-diagonal case the eigenvalues in the first sectors are given for arbitrary values of the boundary parameters.