Entanglement Entropy Bounds in the Higher Spin XXZ Chain

Abstract

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.

27 pages, 4 figures