Entanglement entropy bounds in the higher spin XXZ chain

Abstract

We consider the Heisenberg XXZ spin-J chain (J∈N/2) with anisotropy parameter Δ. Assuming that Δ > 2J and introducing threshold energies EK≔K1−2JΔ, we show that the bipartite entanglement entropy of states belonging to any spectral subspace with energy less than EK+1 satisfies a logarithmically corrected area law with the prefactor (2⌊K/J⌋ − 2). This generalizes the previous results by Beaud and Warzel [J. Math. Phys. 59, 012109 (2018)], as well as by Abdul-Rahman, Fischbacher, and Stolz [Ann. Henri Poincaré 21, 2327 (2020)], who covered the spin-1/2 case.