Fracton topological order via quantum elasticity duality*

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 “fracton order” phenomenon. The disclinations and dislocations respectively map onto charges and dipoles of these gauge theories. The fractionalized mobility of fractons matches the constrained dynamics of lattice topological defects. These dualities lead to predictions 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.

Michael Pretko, Leo Radzihovsky, "Fracton-Elasticity Duality", Phys. Rev. Lett. 120, 195301 (2018);
"Symmetry Enriched Fracton Phases from Supersolid Duality", Phys. Rev. Lett. 121, 235301 (2018).
Leo Radzihovsky, Michael Hermele, "Fractons from vector gauge theory", arXiv:1905.06951