Emergent Elasticity in Amorphous Solids

Jishnu N. Nampoothiri, Yinqiao Wang, Kabir Ramola, Jie Zhang, Subhro Bhattacharjee, Bulbul Chakraborty

Published 2020-04-05Version 1

The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues 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. Here we show that these constraints have the mathematical structure of electromagnetism, where the electrostatic limit successfully captures the anisotropic elasticity of amorphous solids. The emergence of elasticity from 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 stress mapped to electric displacement and forces to vector charges. We present experimental evidence indicating that force chains in granular media are sub-dimensional excitations of amorphous elasticity similar to fractons in quantum spin liquids.