Sufficient Condition for Entanglement Area Laws in Thermodynamically Gapped Spin Systems

TL;DR

This paper proves that in thermodynamically gapped spin systems, the ground states obey the entanglement area law, linking spectral gaps to limited correlations in quantum many-body systems.

Contribution

It provides a sufficient condition under which gapped spin systems exhibit the entanglement area law, enhancing understanding of quantum correlations.

Findings

Ground states of gapped systems obey the entanglement area law.

Spectral gaps restrict correlations in ground states.

Provides an intuitive explanation for the area law in gapped systems.

Abstract

We consider general locally-interacting arbitrary-dimensional lattice spin systems that are gapped for any system size. We show under reasonable conditions that nondegenerate ground states of such systems obey the entanglement area law. In so doing, we offer an intuitive picture on how a spectral gap restricts the correlations that a ground state can accommodate and leads to such a special feature.