  The effect of short-range disorder in nodal line semimetals is studied by
numerically exact means. For arbitrary small disorder, a novel semimetallic
phase is unveiled for which the momentum-space amplitude of the ground-state
wave function is concentrated around the nodal line and follows a multifractal
distribution. At a critical disorder strength, a semimetal to compressible
metal transition occurs, coinciding with a multi- to single-fractality
transition. The universality class of this critical point is characterized by
the correlation length and dynamical exponents. At considerably higher
disorder, an Anderson metal-insulator transition takes place. Our results show
that the nature of the semimetallic phase in non-clean samples is fundamentally
different from a clean nodal semimetal.
