  We study the hierarchical analogue of power-law random band matrices, a
symmetric ensemble of random matrices with independent entries whose variances
decay exponentially in the metric induced by the tree topology on $\mathbb{N}$.
We map out the entirety of the localization regime by proving the localization
of eigenfunctions and Poisson statistics of the suitably scaled eigenvalues.
Our results complement existing works on complete delocalization and random
matrix universality, thereby proving the existence of a phase transition in
this model.
