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

TL;DR

This paper investigates how shear deformations affect holographic amorphous solids, revealing universal scaling relations between shear stress and complexity, and challenging previous assumptions about black hole entropy and complexity.

Contribution

It uncovers a universal scaling relation between shear stress and complexity in amorphous solids under shear, connecting classical elasticity and quantum complexity via holography.

Findings

Shear stress and complexity increase with shear strain.

At large shear, they follow a universal scaling relation.

Provides a counterexample to linear complexity-entropy scaling in black holes.

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.