# Entanglement entropy and particle number cumulants of disordered fermions

## TL;DR

This paper investigates how disorder affects entanglement entropy and particle number fluctuations in noninteracting fermions, revealing universal proportionality and nonanalytic behavior at the Anderson transition.

## Contribution

It provides analytical and numerical analysis of entanglement and cumulants in disordered fermions, highlighting universal relations and critical behavior at the Anderson transition.

## Key findings

- Entanglement entropy and second cumulant are proportional with a universal coefficient in weak disorder.
- Expressions are similar to clean systems but involve a mean free path cutoff.
- Particle number variance and entanglement entropy show nonanalytic behavior at the Anderson transition.

## Abstract

We study the entanglement entropy and particle number cumulants for a system of disordered noninteracting fermions in $d$ dimensions. We show, both analytically and numerically, that for a weak disorder the entanglement entropy and the second cumulant (particle number variance) are proportional to each other with a universal coefficient. The corresponding expressions are analogous to those in the clean case but with a logarithmic factor regularized by the mean free path rather than by the system size. We also determine the scaling of higher cumulants by analytical (weak disorder) and numerical means. Finally, we predict that the particle number variance and the entanglement entropy are nonanalytic functions of disorder at the Anderson transition.