Lower Bound to the Entanglement Entropy of the XXZ Spin Ring

TL;DR

This paper establishes a lower bound on the entanglement entropy of eigenstates in the XXZ spin ring, revealing a logarithmic correction to the area law, and introduces a Combes-Thomas estimate applicable to various quantum operators.

Contribution

It provides a new lower bound on entanglement entropy for the XXZ model and extends Combes-Thomas estimates to more general quantum operators.

Findings

Entanglement entropy follows a logarithmically corrected area law.

Derived a Combes-Thomas estimate for fiber operators.

Applicable to discrete many-particle Schrödinger operators.

Abstract

We study the free XXZ quantum spin model defined on a ring of size $L$ and show that the bipartite entanglement entropy of eigenstates belonging to the first energy band above the vacuum ground state satisfies a logarithmically corrected area law. Along the way, we show a Combes-Thomas estimate for fiber operators which can also be applied to discrete many-particle Schr\"odinger operators on more general translation-invariant graphs.