Quantum Robustness of Fracton Phases

The quantum robustness of fracton phases is investigated by studying theinfluence of quantum fluctuations on the X-Cube model and Haah's code, whichrealize a type-I and type-II fracton phase, respectively. To this end a finiteuniform magnetic field is applied to induce quantum fluctuations in the fractonphase resulting in zero-temperature phase transitions between fracton phasesand polarized phases. Using high-order series expansions and a variationalapproach, all phase transitions are classified as strongly first order, whichturns out to be a consequence of the (partial) immobility of fractonexcitations. Indeed, single fractons as well as few-fracton composites canhardly lower their excitation energy by delocalization due to the intriguingproperties of fracton phases, as demonstrated in this work explicitly in termsof fracton quasi-particles.