Fracton-Elasticity Duality.

Area of Science:

• Condensed Matter Physics
• Quantum Crystal Elasticity
• Fracton Physics

Background:

• Recent studies have explored fractons, a type of quasiparticle with unusual scaling properties.
• Understanding fracton behavior in physical systems remains a key challenge.

Purpose of the Study:

• To establish a concrete link between elasticity theory in 2D quantum crystals and fracton tensor gauge theory.
• To provide a physical realization of the fracton phenomenon in a conventional solid.

Main Methods:

• We mapped topological defects in elasticity theory (disclinations, dislocations) to charges in tensor gauge theory (fractons, dipoles).
• We analyzed the correspondence between crystal phonons and gauge theory modes.
• We investigated the dynamics of lattice defects and their relation to fracton mobility constraints.

Main Results:

• Demonstrated the duality between 2D quantum crystal elasticity and fracton tensor gauge theory.
• Identified topological defects as fractons and dipoles.
• Showed that phonons correspond to gapless gauge modes.
• Predicted new phases and phase transitions in fracton systems, including counterparts to crystal, supersolid, hexatic, and fluid phases.

Conclusions:

• The established duality provides a framework for studying fracton physics in ordinary solids.
• This work predicts novel phases and transitions relevant to condensed matter systems.
• The findings suggest fracton phases are important for understanding interacting topological crystalline insulators.