Hierarchical and ultrametric barriers in the energy landscape of jammed granular matter

TL;DR

This study numerically investigates the energy landscape of jammed granular matter, revealing hierarchical and ultrametric features consistent with mean-field glass theory, despite finite barriers in three-dimensional systems.

Contribution

It provides the first numerical evidence of ultrametric and hierarchical energy landscapes in three-dimensional granular systems near jamming.

Findings

Energy barriers exhibit a scale-free distribution.

Multi-scale distances show ultrametric signatures.

The landscape is hierarchical, supporting theoretical predictions.

Abstract

According to the mean-field glass theory, the (free) energy landscape of disordered systems is hierarchical and ultrametric if they belong to the full-replica-symmetry-breaking universality class. However, examining this theoretical picture in three-dimensional systems remains challenging, where the energy barriers become finite. Here, we numerically explore the energy landscape of granular models near the jamming transition using a saddle dynamics algorithm to locate both local energy minima and saddles. The multi-scale distances and energy barriers between minima are characterized by two metrics, both of which exhibit signatures of an ultrametric space. The scale-free distribution of energy barriers reveals that the landscape is hierarchical.