Emergence of elasticity In amorphous solids: a gauge theory

Amorphous solids that appear in strongly non-equilibrium processes that do not allow thermalization include gels, jammed grains, and even biological tissues. The mechanical response of such disordered solids are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the response of such athermal solids are governed by local conditions of mechanical equilibrium, i.e., force and torque balance of its constituents. In a recent paper [1], we showed that these constraints have the mathematical structure of a generalized electromagnetism. In particular, the electrostatic limit of this theory successfully captures the anisotropic elasticity of amorphous solids and provides a natural explanation for the presence of stress heterogeneities visulaized as "force chains" in granular media. The emergence of elasticity from local mechanical constraints offers a new paradigm for systems with no broken symmetry, analogous to emergent gauge theories of quantum spin liquids. Specifically, our U(1) rank-2 symmetric tensor gauge theory of elasticity translates to the electromagnetism of fractonic phases of matter with the stress mapped to electric displacement and forces to vector charges. I will present results from experiments and numerical simulations that corroborate our theoretical results broadly, present experimental evidence indicating that force chains in granular media are sub-dimensional excitations of amorphous elasticity similar to fractons, and address the long-standing problem of stress transmission in "sandpiles" using the gauge-theory framework.

[1] Jishnu N. Nampoothiri et al, Phys. Rev. Lett., 125, 118002 (2020)