Scale-free non-Hermitian skin effect in a boundary-dissipated spin chain

We study the open XXZ spin chain with a PT-symmetric non-Hermitian boundary field. We find an interaction-induced scale-free non-Hermitian skin effect by using the coordinate Bethe ansatz. The steady state and the ground state in the PT broken phase are constructed, and the formulas of their eigen-energies in the thermodynamic limit are obtained. The differences between the many-body scale-free states and the boundary string states are explored, and the transition between the two at isotropic point is investigated. We also discuss an experimental scheme to verify our results.