I will discuss a recent discovery that elasticity theory of a two-dimensional quantum crystal is dual to a fracton tensor and to a coupled-vector gauge theories, thereby providing a concrete realization of the so-called "fracton quantum order". The disclinations and dislocations respectively map onto charges and dipoles of these gauge theories. The fractionalized mobility of fractons matches the constrained dynamics of crystal's topological defects. These dualities lead to predictions of fractonic phases, and 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.
Winter Qtr. Colloq. committee: M. Schleier-Smith (Chair), B. Cabrera, S. Dimopoulos, T. Heinz, S. Kachru & L. Tompkins
Location: Hewlett Teaching Center, Rm. 200