Universal correlations in vibrational spectra of complex crystals

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 $\mathbf{Q}≠0$ in the Brillouin zone exhibit correlations specific to the GUE universality class.