# Bounds on the bipartite entanglement entropy for oscillator systems with or without disorder

## TL;DR

This paper provides an alternative proof for the area law of entanglement entropy in disordered oscillator systems, using Gaussian state formulas, and compares it with the ordered case where entropy diverges.

## Contribution

It introduces a new proof method for the area law in disordered systems and highlights differences with ordered systems' entanglement behavior.

## Key findings

- Disordered oscillator systems obey an area law for entanglement entropy.
- Ordered oscillator chains can have diverging entanglement entropy.
- The proof uses explicit formulas for Gaussian states instead of negativity.

## Abstract

We give a direct alternative proof of an area law for the entanglement entropy of the ground state of disordered oscillator systems---a result due to Nachtergaele, Sims and Stolz. Instead of studying the logarithmic negativity, we invoke the explicit formula for the entanglement entropy of Gaussian states to derive the upper bound. We also contrast this area law in the disordered case with divergent lower bounds on the entanglement entropy of the ground state of one-dimensional ordered oscillator chains.