  Inspired by the localization phenomenon in condensed matter systems, we
explore constructions in the theory space of multiple scalar fields, in which
exponentially suppressed couplings could originate from random parameters. In
particular, we find a new class of non-local theory space models, in which
scalar fields at non-adjacent sites interact with each other but with strengths
decaying exponentially with the site separation. Such a model could have very
different localization properties, compared to the local theory space scenarios
with only nearest-site interactions, based on the original Anderson
localization model. More specifically, we find that a particular non-local
interaction pattern leads to bi-localization of the two lightest eigenstates.
Exponential localization (and thus exponentially suppressed couplings) then
emerges only and immediately when randomness is introduced, no matter how tiny
it is. We discuss variants of the model and possible UV completions as well.
