  The venerable phenomena of Anderson localization, along with the much more
recent many-body localization, both depend crucially on the presence of
disorder. The latter enters either in the form of quenched disorder in the
parameters of the Hamiltonian, or through a special choice of a disordered
initial state. Here we present a model with localization arising in a very
simple, completely translationally invariant quantum model, with only local
interactions between spins and fermions. By identifying an extensive set of
conserved quantities, we show that the system generates purely dynamically its
own disorder, which gives rise to localization of fermionic degrees of freedom.
Our work gives an answer to a decades old question whether quenched disorder is
a necessary condition for localization. It also offers new insights into the
physics of many-body localization, lattice gauge theories, and quantum
disentangled liquids.
