Logarithmic negativity of the 1D antiferromagnetic spin-1 Heisenberg model with single-ion anisotropy

We study the 1D antiferromagnetic spin-1 Heisenberg XXX model with external magnetic field and single-ion anisotropy on finite chains. We determine the nearest and non-nearest neighbor logarithmic entanglement . Our main result is the disappearance of both for nearest and non-nearest neighbor (next-nearest and next-next-nearest) sites at zero temperature and for low-temperature states. Such disappearance occurs at a critical value of and . The resulting phase diagram for the behavior of LN is discussed in the plane, including a separating line – ending in a triple point – where the energy density is independent on the size. Finally, results for at finite temperature as a function of and are presented and commented.