Report on scipost_202302_00022v1

We study the open XXZ spin chain with a P T -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 P T 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 the isotropic point is investigated.We also discuss an experimental scheme to verify our results.