R-matrix for the XX spin chain at the special imaginary value of staggered magnetic field

Abstract

It is pointed, that the $16\times16$ Hamiltonian density matrix, corresponding to XX spin chain in a staggered magnetic field, satisfies the Reshetikhin condition as well, as the two higher ones. All of them are necessary for the existence of the corresponding $R$-matrix. At the special imaginary value of the staggered field, the $R$-matrix is obtained explicitly. It is shown that the corresponding Hamiltonian has purely imaginary spectrum.