Nonlinear modes disentangle glassy and Goldstone modes in structural glasses

TL;DR

This paper introduces nonlinear glassy modes as a new way to understand low-energy excitations in structural glasses, showing they are robust, quasi-localized, and converge with harmonic modes at low frequencies, providing a clearer picture of glassy dynamics.

Contribution

The authors develop algebraic equations and an iterative method to identify nonlinear glassy modes, offering a new, robust framework for analyzing low-energy excitations in disordered solids.

Findings

Nonlinear glassy modes are quasi-localized low-energy excitations.

These modes converge with harmonic vibrational modes at low frequencies.

Nonlinear modes are unaffected by hybridizations, unlike harmonic modes.

Abstract

One outstanding problem in the physics of glassy solids is understanding the statistics and properties of the low-energy excitations that stem from the disorder that characterizes these systems' microstructure. In this work we introduce a family of algebraic equations whose solutions represent collective displacement directions (modes) in the multi-dimensional configuration space of a structural glass. We explain why solutions of the algebraic equations, coined nonlinear glassy modes, are quasi-localized low-energy excitations. We present an iterative method to solve the algebraic equations, and use it to study the energetic and structural properties of a selected subset of their solutions constructed by starting from a normal mode analysis of the potential energy of a model glass. Our key result is that the structure and energies associated with harmonic glassy vibrational modes and their nonlinear counterparts converge in the limit of very low frequencies. As nonlinear modes never suffer hybridizations, our result implies that the presented theoretical framework constitutes a robust alternative definition of `soft glassy modes' in the thermodynamic limit, in which Goldstone modes overwhelm and destroy the identity of low-frequency harmonic glassy modes.