A random matrix definition of the boson peak

TL;DR

This paper introduces a new class of random matrices called boson peak matrices, which capture the universal eigenvector statistics of the boson peak in glasses and jammed solids, revealing a universal scaling law.

Contribution

It defines a novel class of random matrices that reproduce the universal eigenvector statistics and scaling behavior of the boson peak in disordered solids.

Findings

Eigenvector statistics for boson peak modes are universal.

A new class of random matrices reproduces the boson peak features.

The scaling of the boson peak frequency with coordination number is explained.

Abstract

The density of vibrational states for glasses and jammed solids exhibits universal features, including an excess of modes above the Debye prediction known as the boson peak located at a frequency $\omega^*$ . We show that the eigenvector statistics for boson peak modes are universal, and develop a new definition of the boson peak based on this universality that displays the previously observed characteristic scaling $\omega^*\sim p^{-1/2}$ . We identify a large new class of random matrices that obey a generalized global tranlational invariance constraint and demonstrate that members of this class also have a boson peak with precisely the same universal eigenvector statistics. We denote this class as boson peak random matrices, and conjecture it comprises a new universality class. We characterize the eigenvector statistics as a function of coordination number, and find that one member of this new class reproduces the scaling of $\omega^{*}$ with coordination number that is observed near the jamming transition.