# How much delocalisation is needed for an enhanced area law of the entanglement entropy?

## TL;DR

This paper investigates how delocalisation affects the entanglement entropy in a one-dimensional random dimer model, showing that near critical energies, the entropy surpasses the standard area law with a logarithmic enhancement.

## Contribution

It demonstrates that at critical energies with diverging localisation length, the entanglement entropy follows a logarithmically enhanced area law in the random dimer model.

## Key findings

- Entanglement entropy exhibits a logarithmic enhancement at critical energies.
- The model shows divergence of localisation length at certain energies.
- Enhanced area law is linked to delocalisation phenomena.

## Abstract

We consider the random dimer model in one space dimension with Bernoulli disorder. For sufficiently small disorder, we show that the entanglement entropy exhibits at least a logarithmically enhanced area law if the Fermi energy coincides with a critical energy of the model where the localisation length diverges.