Equivalence of interacting semimetals and low-density many-body systems to single-particle systems with quenched disorder

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.