We consider the Heisenberg XXZ spin-$J$ chain ($J\in\mathbb{ N}/2$) with anisotropy parameter $\Delta$. Assuming that $\Delta>2J$, and introducing threshold energies $E_{ K}:=K\left(1-\frac{ 2J}{ \Delta}\right)$, we show that the bipartite entanglement entropy (EE) of states belonging to any spectral subspace with energy less than $E_{ K+1}$ satisfy a logarithmically corrected area law with prefactor $(2\lfloor K/J\rfloor-2)$. This generalizes previous results by Beaud and Warzel as well as Abdul-Rahman, Stolz and one of the authors, who covered the spin-$1/2$ case.
Categories: math-ph math.MP