Physics Colloquium

I will discuss a recent discovery that elasticity of a two-dimensional quantum crystal is dual to a symmetric tensor gauge theory, thereby providing a realization of the newly discovered "fractonic" quantum order. The disclination and dislocation defects respectively map onto charges and dipoles of the fracton gauge theory. The fractionalized mobility of fractons matches the constrained dynamics of the lattice topological defects. This duality leads to predictions of fractonic phases and quantum phase transitions to their descendants, that are duals of the commensurate crystal, supersolid, smectic, and hexatic liquid crystals. Extensions of this duality to generalized elasticity theories provide a route to discovery of new fractonic models and their potential experimental realizations.