  Recent experimental investigations by M. A{\ss}mann et al. [Nature Mater. 15,
741 (2016)] on the spectrum of magnetoexcitons in cuprous oxide revealed the
statistics of a Gaussian unitary ensemble (GUE). The model of F. Schweiner et
al. [Phys. Rev. Lett. 118, 046401 (2017)], which includes the complete cubic
valence band structure of the solid, can explain the appearance of GUE
statistics if the magnetic field is not oriented in one of the symmetry planes
of the cubic lattice. However, it cannot explain the experimental observation
of GUE statistics for all orientations of the field. In this paper we
investigate the effect of quasi-particle interactions or especially the
exciton-phonon interaction on the level statistics of magnetoexcitons and show
that the motional Stark field induced by the exciton-phonon interaction leads
to the occurrence of GUE statistics for arbitrary orientations of the magnetic
field in agreement with experimental observations. Importantly, the breaking of
all antiunitary symmetries can be explained only by considering both the
exciton-phonon interaction and the cubic crystal lattice.
