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

Interactions-disorder duality and critical phenomena in nodal semimetals, dilute gases and other systems