Exploring the complex free energy landscape of the simplest glass by rheology

Abstract: For amorphous solids, it has been intensely debated whether the traditional view on solids, in terms of the ground state and harmonic low energy excitations on top of it, such as phonons, is still valid. Recent theoretical developments of amorphous solids revealed the possibility of unexpectedly complex free energy landscapes where the simple harmonic picture breaks down. Here we demonstrate that standard rheological techniques can be used as powerful tools to examine non-trivial consequences of such complex free energy landscapes. By extensive numerical simulations on a hard sphere glass under quasi-static shear at finite temperatures, we show that, above the so-called Gardner transition density, the elasticity breaks down, the stress relaxation exhibits slow and aging dynamics, and the apparent shear modulus becomes protocol-dependent. Being designed to be reproducible in laboratories, our approach may trigger explorations of the complex free energy landscapes of a large variety of amorphous materials.