  We study a simple and tractable model of many-body localization. The main
idea is to take a renormalization group perspective in which local entanglement
is removed to reach a product state. The model is built from a random local
unitary which implements a real space renormalization procedure and a fixed
point Hamiltonian with random exponentially decaying interactions. We prove
that every energy eigenstate is localized, that energy is not transported, and
argue that despite being fine tuned, the model is stable to perturbations. We
also show that every energy eigenstate obeys an area law for entanglement
entropy and we consider the dynamics of entanglement entropy under
perturbations. In the case of extensive pertubations we recover a logarithmic
growth of entanglement observed in recent numerical simulations.
