@MISC{Tarasov03onsolutions, author = {V. Tarasov}, title = {On solutions of Bethe equations for the XXZ model}, year = {2003} }

Share

OpenURL

Abstract

Recently certain identities for solutions of the Bethe equations in the six-vertex model were obtained in [FM]. In the note we give an elementary proof of similar identities for the case of the inhomogeneous arbitrary spin XXX or XXZ model. Though the corresponding calculations can be done in the elliptic case too, almost without modification, in that case the resulting identites have rather transcendental form. Even for the case of the six-vertex model the proof of the identities for solutions of the Bethe equations given in the note is simpler than the original proof in [FM]. The detailed exposition of the Bethe ansatz method can be found in [KBI]. The notation used in the note does not coincide with those of [FM] and [KBI], however a reader can easily establish the correspondence. 1. Consider the inhomogeneous XXX model on the N-vertex lattice with the quasiperiodic boundary conditions. Let ℓ1,..., ℓN be the spins of representations at vertices, z1,..., zN — the inhomogeneity parameters, and e µ — the quasiperiodicity parameter, the periodic boundary conditions corresponding to e µ = 1. We assume that 2ℓi ∈ Z>0 for all i = 1,..., N, in other words that all the representations at sites