Entanglement entropy and particle number cumulants of disordered fermions
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.
 Publication:

Annals of Physics
 Pub Date:
 August 2017
 DOI:
 10.1016/j.aop.2017.05.011
 arXiv:
 arXiv:1701.05876
 Bibcode:
 2017AnPhy.383..140B
 Keywords:

 Entanglement;
 Anderson transition;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 19 LaTeX pages, 4 figures, elsarticle style