A symmetry principle for gauge theories with fractons

Fractonic phases are emergent quantum phases of matter that host excitations with restricted mobility. Although these phases have been considered to be of “beyond Landau” order, we show that a certain class of gapless fractonic phases are realized as a result of spontaneous breaking of generalized symmetries. The corresponding symmetries are continuous higher-form symmetries whose conserved charges do not commute with spatial translations, and we refer to them as nonuniform higher-form symmetries. For a given set of nonuniform symmetries, the effective theory associated with the spontaneous breaking of them can be constructed. At low energies, the theories reduce to known higher-rank gauge theories such as scalar/vector charge gauge theories, and the gapless excitations in these theories are interpreted as Nambu–Goldstone modes for higher-form symmetries. Due to the nonuniformity of the symmetry, some of the modes acquire a gap, which is the higher-form analogue of the inverse Higgs mechanism of spacetime symmetries. In this formulation, the mobility restrictions are fully determined by the choice of the commutation relations of charges with translations. This approach allows us to view existing (gapless) fracton models such as the scalar/vector charge gauge theories and their variants from a unified perspective and enables us to engineer theories with desired mobility restrictions.

Field: condensed matter physics
Keywords: fractonic phases, higher-form symmetries, Nambu-Goldstone modes, Higgs mechanism, gauge theories