R-matrix for the XX spin chain in a staggered magnetic field

Abstract

We suggest the elliptic $16\times 16$ R-matrix for the XX spin chain in a staggered magnetic field. This integrable model is a special case of the more general one, studied long ago within the alternative approach by V. M. Kontorovich and V. M. Tsukernik. The Yang-Baxter equation is verified with the full rigorous only in the two special degenerate trigonometric cases. For the general one, studying the first terms of the Taylor expansions for the $R$-matrix entries, we give the strong evidence for implementation of the Yang-Baxter equation.

12 pages