Symmetry enforced fractonicity and $2d$ quantum crystal melting

Understand

Fractons are particles that cannot move in one or more directions without paying energy proportional to their displacement.

• Here, we introduce the concept of symmetry enforced fractonicity, in which particles are fractons in the presence of a global symmetry, but are free to move in its absence.
• A simple example is dislocation defects in a two-dimensional crystal, which are restricted to move only along their Burgers vector due to particle number conservation.
• Utilizing a recently developed dual rank-2 tensor gauge description of elasticity, we show that accounting for their symmetry enforced one-dimensional nature of dislocation motion dramatically alters the structure of quantum crystal melting phase transitions.