  We investigate classes of interacting systems that allow for a mapping to
disordered noninteracting systems. As we show, such a mapping is possible for
interacting systems with a suppressed density of states at the chemical
potential, leading to suppressed screening, and systems near BCS-type
instabilities. The mapping can also be applied qualitatively to other classes
of systems that are not exactly dual to each other. The established duality
suggests a new approach to analytical and numerical studies of many-body and
disorder-driven phenomena in a variety of systems and allows to predict, e.g.,
new phase transitions dual to the previously known ones. Using the established
duality, we predict new disorder-driven transitions in nodal-line semimetals
and systems with long-range hopping dual to, respectively, the BCS and
BEC-vacuum transitions in interacting systems and new interaction-driven
transitions dual to previously known non-Anderson disorder-driven transitions.
The established principle can also be used to classify and describe phase
transitions in dissipative systems described by non-Hermitian Hamiltonians.
