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Elasticity is the ability of an object to withstand the effects of distortion and to return to its original size and shape once the forces causing deformation are removed. When an elastic material deforms under the action of an external force, it experiences internal resistance to the deformation. However, if no external force is applied, it returns to its original state.
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The quantity that describes the deformation of a body under stress is known as strain. Strain is given as a fractional change in either length, volume, or geometry under tensile, volume (also known as bulk), or shear stress, respectively, and is a dimensionless quantity. The strain experienced by a body under tensile or compressive stress is called tensile or compressive strain, respectively. In contrast, the strain experienced under bulk stress and shear stress is known as volume and shear...
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Fracton-Elasticity Duality.

Michael Pretko1, Leo Radzihovsky1

  • 1Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA.

Physical Review Letters
|May 26, 2018
PubMed
Summary
This summary is machine-generated.

We reveal a duality between elasticity theory in 2D quantum crystals and fracton tensor gauge theory. This connection offers a tangible example of fractons in solids and predicts new phases and transitions.

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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.