Universal correlations in vibrational spectra of complex crystals

TL;DR

This paper investigates the spectral statistics of vibrational modes in complex and disordered crystals, revealing universal correlations that follow GOE and GUE classes depending on the crystal structure and wavevector.

Contribution

It uncovers universal spectral correlations in vibrational spectra of complex crystals and disordered solids, linking them to random matrix theory universality classes.

Findings

Eigenmode frequencies in disordered solids follow GOE statistics.

Eigenfrequencies in crystals with complex unit cells follow GUE statistics.

Spectral correlations depend on crystal structure and wavevector.

Abstract

We study spectral statistics of lattice modes in a disordered crystal and in a crystal with a complex unit cell. The correlations of the eigenmode frequencies of a block of a disordered solid is found to obey the GOE Wigner-Dyson statistics. In contrast, the set of eigenfrequencies of a crystal with a complex unit cell taken at the same point ${\bf Q}\not=0$ in the Brillouin zone exhibit correlations specific to the GUE universality class.