Dynamical Localization for Random Band Matrices up to $W\ll N^{1/4}$

Giorgio Cipolloni, Ron Peled, Jeffrey Schenker, Jacob Shapiro

Published 2022-06-11Version 1

We consider a large class of $N\times N$ Gaussian random band matrices with band-width $W$, and prove that for $W \ll N^{1/4}$ they exhibit Anderson localization at all energies. To prove this result, we rely on the fractional moment method, and on the so-called Mermin-Wagner shift (a common tool in statistical mechanics).