An Area Law for the Bipartite Entanglement of Disordered Oscillator Systems

TL;DR

This paper establishes an area law for bipartite entanglement in disordered harmonic oscillator systems, showing that entanglement scales with the boundary surface, applicable to certain gapless models.

Contribution

It proves an area law for entanglement in disordered oscillator systems using logarithmic negativity, extending understanding of entanglement scaling in complex quantum systems.

Findings

Entanglement scales with the boundary surface area.

Applicable to ground and thermal states of disordered systems.

Valid for models that are almost surely gapless in the thermodynamic limit.

Abstract

We prove an upper bound proportional to the surface area for the bipartite entanglement of the ground state and thermal states of harmonic oscillator systems with disorder, as measured by the logarithmic negativity. Our assumptions are satisfied for some standard models that are almost surely gapless in the thermodynamic limit.