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 C. Fischbacher, who covered the spin-$1/2$ case.

MathematicsPhysics

Audience: researchers in the topic

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UCI Mathematical Physics