  The quantum robustness of fracton phases is investigated by studying the
influence of quantum fluctuations on the X-Cube model and Haah's code, which
realize a type-I and type-II fracton phase, respectively. To this end a finite
uniform magnetic field is applied to induce quantum fluctuations in the fracton
phase resulting in zero-temperature phase transitions between fracton phases
and polarized phases. Using high-order series expansions and a variational
approach, all phase transitions are classified as strongly first order, which
turns out to be a consequence of the (partial) immobility of fracton
excitations. Indeed, single fractons as well as few-fracton composites can
hardly lower their excitation energy by delocalization due to the intriguing
properties of fracton phases, as demonstrated in this work explicitly in terms
of fracton quasi-particles.
