Classical elasticity meets quantum complexity: A connection from the holographic lens

Abstract

In this work, we explore the effects of shear deformations in a wide class of holographic amorphous solids. It is found that both the shear stress and the complexity of formation grow with the increase of the shear strain. Notably, in the regime of very large shear, they exhibit coordinated behavior and adhere to a universal scaling relation, uncovering a surprising connection between two seemingly unrelated aspects of amorphous systems. Furthermore, our findings also provide a counterexample to the previous understanding that the complexity scales linearly with the Bekenstein-Hawking entropy for large static black holes.