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

TL;DR

This paper derives an explicit R-matrix for the XX spin chain in a specific imaginary staggered magnetic field, revealing that the Hamiltonian has a purely imaginary spectrum, which advances understanding of integrable models with complex parameters.

Contribution

The paper explicitly constructs the R-matrix for the XX spin chain at a special imaginary magnetic field, demonstrating the integrability conditions and spectral properties.

Findings

R-matrix explicitly obtained at special imaginary field

Hamiltonian exhibits purely imaginary spectrum

Satisfies Reshetikhin condition for integrability

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.