Entanglement Entropy Bounds in the Higher Spin XXZ Chain

We consider the Heisenberg XXZ spin-$J$ chain ($Jinmathbb{N}/2$) with anisotropy parameter $Delta$. Assuming that $Delta>2J$, and introducing threshold energies $E_{K}:=Kleft(1-frac{2J}{Delta}right)$, 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 $(2lfloor K/Jrfloor-2)$. 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.