Solution of the vertex model with non-diagonal open boundaries

Abstract

We diagonalize the double-row transfer matrix of the SU (N ) vertex model for certain classes of non-diagonal boundary conditions. We derive explicit expressions for the corresponding eigenvectors and eigenvalues by means of the algebraic Bethe ansatz approach.

An(1)affine Toda field theories with integrable boundary conditions revisited

“…It is however clear that another possibility arises, that is the implementation of certain boundary conditions that lead to the reflection of a soliton to itself in imaginary ATFT or to the reflection of a fundamental particle to its conjugate in real ATFT. These boundary conditions are known as soliton preserving and have been extensively analyzed in the frame of integrable quantum spin chains [21,22], [26]- [30].…”

Nested off-diagonal Bethe ansatz and exact solutions of the su(n) spin chain with generic integrable boundaries

“…Some remarks are in order. When M andM commute with each other and thus can be diagonalized simultaneously by some gauge transformation, the corresponding open spin JHEP04(2014)143 chain can be diagonalized by the algebraic Bethe ansatz method after a global gauge transformation [71]. In case of the boundary parameters (which are related to the matrices M andM ) have some constraints so that a proper "local vacuum state" exists, the generalized algebraic Bethe ansatz method [41,77,78] can be used to obtain the Bethe ansatz solutions of the associated open spin chains [79][80][81].…”

Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms

“…. ,N } satisfy the following BAEs 18) where the function Q 2 (u) is given by (4.11). The non-singular property of the T − Q ansatz (4.9) at the points (4.17) can be verified by directly calculating the residues of the ansatz at these points.…”

“…However, it has been well known for many years that there exists a quite usual class of integrable models, which do not possess U(1)-symmetry and thus make the conventional Bethe ansatz methods almost inapplicable. Some famous examples are the closed XYZ chain with odd number of sites [9], the anisotropic spin torus [10], the quantum spin chains with nondiagonal boundary fields [11][12][13][14][15] and their multi-component generalizations [16][17][18][19][20][21]. The broken U(1)-symmetry in those models leads to the absence of an obvious reference state, which is crucial for the usage of the conventional Bethe ansatz (BA) methods [1,9,[22][23][24][25][26][27][28].…”