Abstract
We study theoretically and numerically the entanglement entropy of the -dimensional free fermions whose one-body Hamiltonian is the Anderson model. Using the basic facts of the exponential Anderson localization, we show first that the disorder averaged entanglement entropy of the dimension cube of side length admits the area law scaling , even in the gapless case, thereby manifesting the area law in the mean for our model. For and we obtain then asymptotic bounds for the entanglement entropy of typical realizations of disorder and use them to show that the entanglement entropy is not self-averaging, i.e., has nonvanishing random fluctuations even if .
- Received 14 June 2014
DOI:https://doi.org/10.1103/PhysRevLett.113.150404
© 2014 American Physical Society