Crystal-to-fracton tensor gauge theory dualities

Abstract

Fractons are a new class of emergent quasiparticles with restricted mobility. Previously, fractons were only known to occur in complicated spin models without direct material realization. Here, the authors detail various duality relationships, which map directly the physics of fractons onto topological defects of quantum crystals. Fractons and dipoles correspond to disclinations and dislocations, respectively, while elastic phonons map onto tensor gauge modes. The authors discuss several applications of the duality, such as a simplified reformulation of two-dimensional melting.