General boundary conditions for the and open spin chains

Abstract

Two types of boundary conditions ('soliton preserving' and 'soliton non-preserving') are investigated for the sl(N ) and sl(M|N ) open spin chains. The appropriate reflection equations are formulated and the corresponding solutions are classified. The symmetry and the Bethe ansatz equations are derived for each case.The general treatment for non-diagonal reflection matrices associated with the 'soliton preserving' case is worked out. The connection between the 'soliton non-preserving' boundary conditions and the twisted (super-) Yangians is also discussed.

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

“…Note also that in the expressions for the boundary Hamiltonian written above there exist no free boundary parameter, contrary to the SP case as will see subsequently. Analogous results may be seen in the context of quantum integrable spin chains regarding the explicit expression of the corresponding Hamiltonians as well as their symmetries [31,21,22].…”

“…Note however that in quantum spin chains in addition to the well studied SP boundaries SNP boundary conditions were first introduced in [31] and further analyzed and generalized in [21,22,24,25]. It is thus our primary objective here to complete the study of integrable boundary conditions in ATFT by introducing and fully analyzing the novel (SP) boundary conditions.…”

Solution of the vertex model with non-diagonal open boundaries

“…We note that similar result has recently been reported in ref. [16] however on the basis of the analytical Bethe ansatz method and solely for case of diagonal boundaries.…”

“…Therefore, we expect that the method devised in this work will be useful in the solution of the eigenspectrum of a variety of isotropic systems with certain nondiagonal open boundaries. Interesting examples would be the case of soliton non-preserving boundaries [16,18] for the conjugated representation of the SU(N) as well as general boundaries for vertex models invariant by the O(N) and Sp(2N) Lie algebras.…”

Reflection equation for theN= 3 Cremmer–GervaisR-matrix

“…Up to now, there are many works about the reflection equation [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Taking the XXZ chain for example, the diagonal solution was obtained in [1,2], the general solution in [3].…”