  Describing collective behaviour of a large number of interacting particles is
one of the biggest challenges in physics and is key to understanding phase
transitions and transport and thermodynamic properties in systems with strong
particle correlations. We demonstrate that a broad class of interacting
disorder-free systems, such as nodal semimetals (e.g. graphene, Weyl,
nodal-line semimetals) and dilute interacting gases, can be mapped to
non-interacting systems with quenched disorder. The interacting systems that
allow for such a mapping include systems with a small single-particle density
of states at the chemical potential (e.g. near the nodal point or a nodal line
in a topological semimetal), which leads to a suppressed screening of the
interactions. The established duality suggests a new approach for analytical
and numerical studies of many-body phenomena in a class of interacting
disorder-free systems by reducing them to single-particle problems. It allows
one to predict, describe and classify many-body phenomena by mapping them to
the effects known for disordered non-interacting systems. We illustrate the
mapping by showing that clean semimetals with attractive interactions exhibit
interaction-driven transitions at low temperatures in the same universality
classes as the non-Anderson disorder-driven transitions predicted in
high-dimensional non-interacting semimetals. Furthermore, we find a new
non-Anderson disorder-driven transition dual to a previously known
interaction-driven transition in clean bosonic gases. The established principle
may also be used to classify and describe phase transitions in dissipative
systems described by non-Hermitian Hamiltonians.
