Entanglement Entropy Bounds in the Higher Spin XXZ Chain

TL;DR

This paper establishes bounds on the entanglement entropy in higher spin XXZ chains, showing a logarithmic area law for states below certain energy thresholds, extending previous spin-1/2 results.

Contribution

It generalizes entanglement entropy bounds from spin-1/2 to higher spins in the XXZ chain under specific anisotropy conditions.

Findings

Entanglement entropy obeys a logarithmic area law for energies below E_{K+1}.

Prefactor of the entropy bound depends on the spin and spectral subspace.

Results extend previous spin-1/2 bounds to higher spin cases.

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.